business statistics

PRESTON UNIVERSITY

TERMINAL EXAMINATION

S t u d e n t N a m e : I s lamabad — K o h a t - P e s h a w a r - Laho re

i R e g . fmr

Course Code: Course Title: Program: Semester:

QM 4354 Business Statistics MBA/MS Summer 2011

PRE:S .''ON UNIVERSITY -LIBRARY

This is a three-hour examination and consists of review questions and problems. You may a t tempt not more than a total of ten review questions and problems.

Q. I a) Write and explain briefly the fields of Singular Statistics, b) Define any FOUR of the following with examples:

i. Error ii. Class-width iii. Frequency distribution table v. Class-limits

iv. Simple Random Sample

Q.2 a) Define with examples; i. Median ii. Mode iii. Variance b) Differentiate between Mutually and Non-Mutually exclusive events with examples.

Q.3 a) Assuming the following approximate numbers are correctly written, how many significant digits does each have? (a) 21.80; (b) 0.0162; (c) 0.085 billion; (d) 4.00; (e) 1002.3; (f) 0.005.

b) Round the following to three significant digits: i. 307.42 ii. 0.046874 iii. 128,502.81 iv. 3.055 v. 21.3172

Q.4 From the following table compute; i, Coefficient of variance ii. 1QR iii.

Weight / 6 5 - 84 9 8 5 - 1 0 4 10

1 0 5 - 1 2 4 17 1 2 5 - 1 4 4 10 1 4 5 - 1 6 4 5 1 6 5 - 1 8 4 4 185 - 2 0 4 5

Q.5

Q.6

Q.7

Using the table of Q# 4, compute; i. Geometric mean ii. MAD from Median iii.P73

Draw Histogram and Frequency Polygon on graph paper only Daily wages (Rs.) 4 - 6 6 - 8 8 - 1 0 1 0 - 12 1 2 - 1 4 1 4 - 1 6 No. of employees 13 111 182 105 19 7

Make a frequency distribution table using 10 as the class-interval and start first-class from 130 onwards: WEEKLY EARNINGS OF 50 MANUFACTURING WORKERS, IN DOLLARS

151 179 163 142 180 195 150 206 194 343 211 193 194 198 187 164 188 175 198 216 182 163 180 155 178 209 172 208 190 185 148 205 158 195 192 184 174 161 199 165 209 206 187 163 131 202 137 179 200 156

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Q.8 (a) An investor thinks the probability that stock A will rise in price is 0.7 and the c o r r e s p o n d ^ probability for stock B is 0.4. The probability that both prices will rise is 0.3. Write the symbolic rule for, and calculate the probability that, A or B will rise, (b) Using A, B, A ' , and B ' as classifications, make a complete table of probabilities (c) The answer to (a) is the sum of the probabilities of what joint events? (d) Verify that P(A or B) = 1 - P(A13'). Why would this relationship always hold for two events?

Q.9 a) A contractor has bid on two contracts, A and B. The probability of winning A is assessed at 0.5 and the probability of winning B if A is won is 0.7. Write the symbols for the rule, and compute the probability that the company wins both contracts,

b) A contractor bids on two contracts A and B, assessing the chances of winning at 0.5 and 0.6 for A and B, respectively, and the chance winning both at 0.2. What is the chance of winning A or B?

Q.10 Following Table shows the binomial distribution for n = 4 and p = 0.3.

P(r) 0.2401 0.4116 0.2646 0.0756 0.0081 Compute Mean and Variance of the Binomial Prob-distribution.

Q.I la) An area has hurricane once in 10 years, on the average, and the hurricane arrivals are a Poisson process. What is the probability that in the next four years there will be (a) exactly one hurricane? (b) at least two hurricanes?

b) Five of the 24 seemingly identical diamonds on display at Short's Jewelers are of excellent (flawless) quality, and the remainder have slight imperfections. Jan Long purchased four randomly selected diamonds to store in a safe-deposit box as an investment. Compute the probability distribution for the numbers of excellent diamonds Jan purchased.

Q. 12 Using the normal approximation of the binomial. Fifty-three percent of the stockholders in Bim, Inc., are in favor of a mergers with Big Deal, Inc. What is the probability that in a sample of 100 stockholders less than half will be in favor of the merger?

Q.I3 Assuming mileages obtained by a certain brand of tire are uniformly distributed with a mean of 25,000 miles and a range of 10,000 miles, (a) what are the upper and lower limits of tire mileages? (b) What is the probability that a tire will last 26,000 miles or more.

Q.14 Bill Peters has observed that when he leaves the office at the end of the day, he has to wait an average of 4 minutes to get an elevator. Assume elevator arrivals are a Poisson process, (a) What is the value of V? What is the unit of time? (b) What is the probability that Bill will have to wait from 2 to 4 minutes for an elevator? (c) What is the probability that Bill have to wait more than 8 minutes for an elevator?

Q.15 A population consists of 5 elements 2, 4, 6, 8,10. Draw all possible samples of size 3 and compute; i. Mean of samples ii. Determine the sampling distribution of means. iii. Compute Mean of Means and verify that

r 0 2 3 4

o f 2

PRESTON UNIVERSITY

TERMINAL

S t u d e n t N a m e : iiSamabtid - Kohat - Peshawar - Lahore

Ueg. No:_


QM 4354 Business Statistics MBA/MS-IT Fall 2010 PRESTON

UNIVERSITY LIBRARY This is a three-hour examination and consists of review questions and ; problems.

You may attempt not more than a total often review questions and problems.

Q.l a) Distinguish between statistics plural and statistics singular. b) What is the d i s s interval for a frequency distribution which has classes 0.00 - 24.99, 25.00 - 49.99,

and soon.

Q.3 For the data in table below, make a frequency distribution table:

Q.4

Q.5

Q.5

Q.6

Q.7

Q.8

151 179 163 142 180 195 150 206 194 143 . 211 193 194 198 187 164 188 175 198 216 182 163 180 155 178 209 172 ' 208 190 185 148 205 158 195 192 184 174 161 199 165 209 206 187 163 131 202 137 179 200 156

A truck carried 22 tons of cargo a distance of 300 miles. Operating expanses (driver, gas etc.) were $190. Compare operating expenses per ton-mile.

Use table hi Q#2 and make a Stem and Leaf Table and write the data in ordered form.

Define Class Mark. Fill the table with class marks.

Output per Labor Hour Class Mark (?) ! No. of Days per. 4 . 0 - 4 . 9 5 .0 -5 .9 6,0 - 6.9 ? .0^7 .9 8 .0 -8 .9 9 . 0 - 9 . 9

11 17 16 8 5

Last month an investor acquired 500 shares of a stock at an average price.'of $42 per share, tiiis month the investor bought 300 shares of the stock at an average price of $36 per share. Find the average price per share paid during the 2 months.

Mdrith-to-rrionth changes in the prices of a stock were 11, 18, and — 15 percent. Using the geometric meah.of the growth factors, determine the average monthly parentage change in the price of the stock! ' '

608 employees of a firm were asked if they would favor cutting their lunch hour by VV.hour so that they eoutd leave work that much earlier. The results are shown in the following table:

Favor (P) . Disfavor (D) Neutral (N) " Men(M) . 84 .12 - . .24 Women(W) 204 ; 180 , . . 96

If a randomly selected employee is a man, what is the probability that he is neutral?

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Q.9 The probability of finding oil in an area is 0.15 if the underlying stratum has a dome structure. What is the probability of hot finding oil if there is a dome structure? ;

Q. 10 If we toss two fair coins simultaneously what is the probability of getting exactly one Head?

Q.I 1 If 60 percent of the voters in a large district prefer candidate Jordan, what is the prfcbability.that in a • sample of 12 voters exactly 7 will prefer Jordan.

Q.12 A filling machine is set to pour 592 ml of water into bottles. The amount of fill is normally distributed 'with a mean of 592 ml and a standard deviation of 4 ml. Use standard Normal tale to find the probability that a bottle contains between 952 and 956 ml.

Q.13 Assume that the diameters of the shafts made by an automatic machine are normally distributed with a p. = 25 and a = 0.5?mm. What is the probability that a shaft will have a diameter between 25.2 to 25.9 mm?

Q.J 4 The weight of maple sugar obtained by boiling down a tank of maple-tree sap is uniformly distributed with the mean of 10 pounds and range of ) .8 pounds. i. What are the smallest and largest weights of sugar obtained from a tank of SBp?

ii. What is the probability that a tank of sap boil down to between 9 and 10.5 pounds?

Q.I 5 How many samples of size 4 can be drawn from the population 0, 3, 6, 3,18? Compute the sampling distribution of the mean.

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U n i t s Uu£iir"Hii PRESTON UNIVERSITY

*^SaS^6* K o h a t - I s l a m a b a d - L a h o r e


- P e s h a w a r - f a i s a l a b a d



This is a three-hour examination and consists of review questions and problems. You may attempt not more than a total of ten review questions and problems.

Q.l

Q.2a)

Define any five of the following and cite examples: i. Error ii. Non-Mntually Exclusive Events iii. Mode v. Sample Space

iv. Statistical Inference

b)

During a month when a scheduled 500-mile flight was token on 25 days by a plane having 240 available passenger-seats, 60 percent of the seats, on the average, were occupied. Passenger operating revenue for the period was $100,818. Compute revenue per passenger-mile. Sales which actually totaled 9100 units for the current month had been predicted earlier at 10,000 units. Compute the percent error.

Q.3 Make a frequency distribution table using 9.0 as the class-interval and start first class from 130 onwards.

151 179 163 142 180 195 150 206 194 143 • 211 193 t94 198, 187 164 188 175 198 216 182 t63 180 155 178 209 172 208 190 185 148 205 158 195 192 184 174 161 199 165 209 206 187 163; 131 202 137 179 200 156

Q.4 From tha table given below compute; i. MAD from Mean ii. Coefficient of Variance

Rent. Dollars per month Numbers of apartments

250 - 274 8 275 -299 23 300-324 52 325-349 : 86 350-374 63 375-399 ; 56 •1110 - 424 : 37 425-449 • 26 4 5 0 - 474 i ' 11 4*5-499 ' 7

Q5

Q.6

Compute Mode, Median and Geometric Means from data given below* 23 /11 , 40, 35, 69, 75, 80, 105, 36, 8 '

The probability* of finding oil m an area where the underlying rock formation has 4 dome structure is 0.3. gasedupon soundings,'a geologist states the probability that a dome structure exists is 0:8.

(a) What is the probability that the dome structure exists and oil will be foitrnd? (b)Using F and D, respectively, for find oil and dome exists, write the relevant symbolic probability rule for (a)'

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I

Q.7 If A and B ate independent wilh P{A) = 0.3 and P(B) = 0.4, calculate P{A or B). Explain the method used.

Q.8 If a coin is tossed 20 times (a) What is the expected number of heads? (b) What is the probability that the number of heads will turn out to be the expected number? ';

Q.9 If 04 percent of a bank's account balances are in error and a sample of 200 accounts is selected, find the probability that (a) none of the 200 balances is in error, (b) exactly one balance is in error; (c) at least three balances arcin error; (d) the number of balances in error is from two to five, inclusive; (e) fewer than •four balances are in em». i :.

Q.10 In an audit of accounts of Jordan-HoKman, a large department store, it is decided Qist to check a sample of 1000 accounts, and tHen to carry out a more detailed study if the number of sample accounts in error exceeds 15. One percent of alf Jordan-Holtnian accounts contain errors. What is the probability that the sample audit results will lead to a more detailed study?

Q. 11 Suppose that the weight of maple sugar obtained by boiling down a tank of ample-tree sap is uniforhiry distributed with a mean of 10 pounds and a range of 1.8 pounds, (a) What are the smallest and largest weights of sugar obtained Irom a tank of sap? What'is the probability that a tank of sap will boil down to between 9 and 10.5 pounds? '

Q.12 The cylinder-making machine has o = 0.5 mm. At what mean value JJ. should the machine be set to ensure that only 2.5 percent of the cylinders have diameters of 25 .48 mm or more?

Q.13 A population consists of five elements 2,3, 6, 5,10. Draw all positive samples of size 3. i. Compute the proportion for even numbers ii. Make a sampling distribution of proportions and verify that

a. u - =P b-

Q.14 Using table given below, draw graph paper only.

i. Histogram ii; Cumulative frequency polygon (Topped-Bottom). On

Out put per labor-hour Number of days 4.0^1.4 1 4.5-4.9 5.0-5.4 3 5.5-3.9 8 . 6.0-6.4 6 6,5-6.9 11 7.0-7.4 9 7.5-7.9 7 8.0-8.4 5 8.5-8.9 3 9.0-9.4 4 9.5-9.9 1

Frequency total 60~*

Q. 15 Define and give examples: i. Class — Boundaries ii. Geometric mean iii. Statistics in the plural sense iv. Simple random sample.

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PRESTQM ' i w v i i i - ^ UNIVERSITY EXAMINATION Kohat - Islamabad - Lahore - Peshawar - Faisalabad

Course Code: QM43S4 Course Tide: Business Statistics Program: MBA/MS Semester: Summer 2009

This U a three-hour examination and consists of review questions and problems. You may at tempt not more than a total of ten review questions and problems.

Q. 1 Define any FOUR of the following with examples: i. Error ii. Class-interval iii.Mutually exclusive events iv. Sample-Space v. Dependent-Events vi. Population and Sample

Q.2 a) Distinguish between statistics plural and statistics singular, b) What is a simple random sample? c) With what type of decision is statistical decision analysis concerned?

Q.3 a) Prom the data given in the following table, present a tabular comparison cf the percentage distribution of sales by region for the 2 years. Round to the first decimal place:

Sales, thousands of dollars

Region This year Last year

East • $2465 $2415 Central 2084 1814 West 1391 998

b) Round the following to three significant digits (a) 408.52; (b)0.036972; (c)237,401,62; (d) 1.065; (e) 1.055; (f) 24,449.

Q.4 UaingihetabIeofQ#6 Draw i. Histogram ' • ii. Cumulative frequency polygon (Topped to Bottom) '

Q.5 Make1 ajfrequency table using 8,0 as the lower limit of the first class and with a width of 1 unit, convert it to a frequency distribution: > '

9.0 4t.fi *1,7 10.1 12.3 10,5

10.2 U.3 12.1 10.7 13.8 . 10.8 13.6 - 16.4 11.0 15.8 9.3 13.7 11:0 ' 8.0 12.0 11."5 9,7 11.6 14,1. 10.0 9.9 tt.4 15.7 11.5 9.8 13.0 9.1 8.3 12.9 14.0

13,2 10.S 106 12.5 15.1 12.8

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Q 6 Using the taple given below, compute; i.C.V ii.IQR iii. P 6 3 and D 3

Rent, Dollars;per mouth Numbers of apartments. 250-274 6 275-299 23 300-324 52 325-349 36 350-374 68 375-3*19 56 400 -424 37 425-449 26 450 -414 11 475-499 7

Q.7 From the table given below compute: i. MAD from Median ii. Geometric Mean iii. Moote TABLE: ; , * Frequency Distribution for output per labour-hour

Output per labor hour Number of days 4.0 - 4.4 1 4 . 5 - 4 . 9 2 5 .0-5 .4 3 5 .5-5 .9 8 6 .0 -6 .4 6 6.5 - 6.9 n 7 .0-7 .4 9 7 .5 -7 .9 7 8 .0-8 .4 5 8.5 - 8.9 3 9 .0 -9 .4 4 9 .5-9 .9 1

Frequency total: 60

Q.8 The probability of finding oil in an area is 0.15 if the.underlying stratum has a dome structure.. What is the probability of not finding oil if there is a dome structure?

Q.9 a) KP(Q/S) = 0.25 &ndP(QS) = Q.l, find P(S). b) Let B,R'Q, O'be two events and their complements, (a) What joint event constitute R of Q7 (b)Whatis

the complement of R or g? (c) Complete the following: P{R or g ) = 1 - P( >.

A motel has 45 rooms available on a particular night. In as much as 10 percent of the large population of those making motel reservations fail to show up, the motel makes 50 reservations for tliis particular night Use the binomial distribution to find the probability that rooms will be available for all those who do show up. One percent of the oysters found by native divers off Palm Tree Atoll contain a pearl. If Captain Cruiser buys 40 Oysters, what is the probability that he will obtain at least three pearl-bearing Oysters?

Q.l la) A bird arose early one morning and ate five of the 20 cherries remaining on a cherry tree,. Four of the 20 cherries contained a worm. What is the probability that the early bird got three or more worms?

b) An area has a hurricane once in 10 years, on the average, and hurricane arrivals are a Poison process. What is the probability mat in the next 4 years there will be (a) exactly one hurricane? (b) at least two hurricanes?

Pago 2ot3

]

Q. 12 Assuming mileages obtained by a certain brand of tire are uniformly distributed with a mean of 25,000 miles and a rang of 10,000 miles, (a) what are the upper and lower limits of tire mileages? (b) what is the probability that a tire will last 26,000 miles or more?

Q.13 Fordbart Casualty Co. insures a large number of buildings for fire damage. On the average, Fordhart lias to pay eight-damage claims of over$l million each year. The Company is short of cash and will have to sell some of its securities to get cash if it has to pay a damage claim of more than $1 million during the next 3 months. Assuming damage claims over $1 million are a Poisson process, what is the probability that the Fordhart will have to sell securities.

Q.14 Some people who make reservations for air travel do not show up for their scheduled flight. Airlines may make allowances for these "no shows" by booking reservations for more persons than can be accommodated on a flight. If 4 percent of the large population of reservations turn out to be no-shows, and 350 reservations are made for a particular flight on a plane seating 340, what is the probability that seats will be available for all those who do show up for the flight?(UseNAB to solve)

Q.15 A population consists of 6-elements 0,3,6,7,10,13, i. Draw all possible samples of size 3.

1 ii. Make a Sampling Distribution of proportions using odd numbers as a success, iii. Verify that;

fPQ

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•RKSTON NIVERSITY


hu t - I s l amabad - Laho re - P e s h a w a r - Paisalabad

Course Code: Couise Title: Program: Sem :ster: ,


Thls-is a i h r e V h o u r examination and consists of review questions and problems. You may attt mpt not more thnn a total of ten review questions and problems.

Q. I a) Diatin] ulsh between statistics plural and statistics singular. b) What i i the a simple random sample? c) What, k a statistical inference?

Q.2a)

b)

a. A pi ice of $99.95 is to be reduced by 20 percent. Show two ways to compute the new price b. Sales this year ai E $20,900 compared with $22,000 last year. Compute and describe the percent change in sales form last ye IT to this year. Use Tible given below to compute percentage relatives. Round to the first decimal place, (a) Take period 1 equal ip 100 (b) Take the average of periods 1 and 2 = 100 TABIC Peri Price, cents per gallon

1 73.9

~ ~ 2 ~ 77.9

3 83.9

4 8.9

Q.3 Make a frequency table using 21 as the class-interval and start first class-from 85-105.

165 156 136 H i 9

Q4

O Q.5

Using

186 122 172 140 114 113 135 131 127 112 188 171 90 187 136 159

170 111 147 165

153 208 125 177 179 152

103 T59~

169 136 155 8_5_

150

he table of #6, draw Cumulative frequency polygon (Topped -Bottom) and Histogram.

The c< sts per load (in cents) of 35 laundry detergents tested by a consumer organization are shown below Table

CI iss Limits

13-19 ; 10-26 27-33

'14-40 H - 4 7 *8-54 S5-61 52-68

2 7

12 5 6 1 0 2

Cornp rie: i. C.V. li. I Q l iii. MAD from Median

Q.6 Using table given below representing light bulbs to determine their life times (in - hows). Compute i. andFjTv ji. Moic iii. Geometric mean iv. Average

Class - Boundaries 52.5 - 63.5 6 63.5- 74.5 12 74 .5- 85.5 25 85.5-96.5 18 96.^-107.5 14

107.<S-118.5 5

Q.7 The probability that it will be colder tomorrow is 0.6 and the probability it will snow if it gets cojder is 0.7. What is the probability that ii will colder and snow tomorrow?

i Q.8 A tire Supplier has 10 tires in stock. Although they ali look alike, two of them are retreads and eight are

new. (^) If a buyer selects two at random, what is the probability that both are new? Both retreads? (b) If a buyer Selects four, what is the probability that at least one is a retread? :

Q.9 a) A secretary types' 75 words per minute and averages six errors per hour of typing. Assuming error occurrences ore a Poisson process, what is the probability that a 225-word letter will be typed without error,

b) Threelpercent of the large number of tires made by a manufacturer are defective. If a store buys 100 of these tires, what is the probability that the number of defectives received is (a) zero? (b) less than three*? (c) more than six7

i

Q.10 The probability of success on a binomial trial is 0.10. Porn •= 50 trials, find the probability that the number of successes will be (a) less than five; (b) at least five; (c) at most five; (o) more than three; (e) a[ least two, but less than seven; (f) form zero to five, inclusive;(g) exactly six, (Iv) at least 10.

Q.ll If 55 percent of the voters in an area favor a particular candidate, what is the probability that, in a sample of200] voters, less man half would favor the candidate?Note: (Use NAB to solve Q# 11).

Q.I2 A random variable takes on values symbolized by x. If the available is normally distributed with a mean of 50 arid a standard deviation of 4 what is the probability that x will be in the following intervals?- • i. 50 to 54 ii. 45 to 54 iii. 53 to 58 iv. more than 60 v. less than 45 vi. more than 45

Q.13a) Assuming mileages obtained by a certain brand of tire uniformly distributed with a mean of25,000 miles andafange of 10,000 miles (a) what are the upper and lower limits of tire mileages? (b) What is the probability that a tire will last 26,000 miles or more7

b) Bill Peters has observed that when be leaves the office at the end of die day. lie lias to wait an average of 4 minutes to get an elevator. Assume elevator arrivals are a Poisson process- (a) What is the value of X? What is the unit of time? (b) What is the probability that Bill will have to waif, from 2 to 4 minutes for an elevator? (c) What is the probability that Bill have to wait more man 8 minutes for an elevator?

Q.I4 A population consists offive elements 2,3,5,6 and ! 1. i. Draw all possible samples of size 3 (without replacement). . . . ii. Compute the prnrje/l^es for odd nnmbws. " iii. Make a sampling distribution of properties and verify that ~j -

a. u - -P b. a - = . / — . J ; p " If n VjJV-1

Q.15 Define any FOUR of the following; i. Sample - space ii. Mutually Exclusive Events iii. Enoi iv. Subjective - Probability v. Dependent - Events vi. Discrete ad Continuous Variables.

PRESTON UNIVERSITY

^ j ^ ^ ^ g ^ Kohat - Islamabad - Peshawar


— Lahore - Faisalabatl — Multan — Gujrmiwala


QM 4354 Business Statistics MBA/MS Fall 2007

This Is a three-hour examination and consists of review questions and problems. You may attempt not more than, a total of ten review questions and problems.

Q.l Explain any FOUR of the following: i. Statistical Inference ii. Decision Analysis iii. Sample Random Sample iv. Population and Error v. Uses of Statistics

Q.2 a) Compute percentage relatives for the board feet prices in the following Table. Round to the first decimal place. i. Take period 2 as 100. ii. Take the average of periods 1 through 3 as 100. TABLE:

Period 1 2 3 4 5 Price per 1000 board feet £130.25 $154.98 $174.35 $150.62 $125.63

b) Unemployment at the end of a year was 7.1 percent of the civilian labor force. At the beginning of • year it; had been predicted that die figure would reach 7.4 peicent by the year's end. By how much was

the prediction in error i. In percentage points ii. In percent? — — — — —

Q.3 Draw Histogram and Frequency Polygon from the following Table.(Use graph paper only). TABLE

Rent, dollars per month No of apartment

.. 2^0-274 ' 8 ' 275 - 299 23 300-324 52 325 - 349 86 3S0-374 68 375 - 399 56 400 - 424 37 . 4iS - 449 26 .

; 4^0-474 11 . 475 - 499 7

Q.4 Mafctf a frequency table using 5.0 as the class-interval and start first class rrom48.0 - 52.0 onwards

71.6 95.5 73.0 74.2 81. S 90.6 55.9 81.9 68.9 74.2 80.7 65.7 67,6 82.<t 77.8 69.4 S3.2 82.7 73.S 64.2 63.9 48.6 83.5 70.8 72.1 71.6 59.4 77.6

Q.5 From the follow table compute i. Mad from Median ii. Geometric Mean iii. iQR

Weight f . 6 5 - 8 4 9

8 5 - 1 0 4 10 105 - 124 17 125 - 144 10 145-164 5 165-184 4 185 - 204 5

Q.6 Using the Table of Q#5, compute; i. Coefficient of Variance ii. Mode iii. D.i and P 6 1

Q.7 a) In a firm, 20 percent of the employees have accounting back grounds, while 5 percent of the employees are executives and have accounting backgrounds. If an employee has an accounting background, what is the probability that the employee is an executive?

b) A contractor has bid on two contracts, A and B. The probability of winning A is assessed at 0.5 and the probability of winning B if A is won is 0.7. Write the symbols for the rule, and compute the probability that the company wins both contracts.

Q.S Compute Mean and Standard Deviation form the following table;

' r 0 1 ~~T~ 3~~~ 4

" > ( r ) 0.2401 0.4116 0.2646 0.0756 0.0081

Q.9 a) Calls at a telephone switchboard follow a Poisson process and occur at an average rate of six calls per 10 minutes. The operator leaves for a 5-niinute coffee break, (a) What is the value of U7 What is the probability thai exactly two calls come in (and so go unanswered) while the operator is away? What is the probability that more man three calls go unanswered?

b) Oil-drilling rights at. 25 sites on government-owned property have been sold to oil companies. The sites are to be assigned at random to the companies. Oil Ventures, Inc, which has purchased leases for four sites, has a preference for three of the 25 sites. What is the probability that Oil Ventures gets at least two of its preferred sites?

Q. 10 A test has 25 true-false questions. A student flip's a coin for each question and checks true if heads show and false if tails show. If 1 7 or mote correct is passing, what is the change that this student will pass? Use Normal Approximation of Binomial (NAB). • .

. Q. 11 Suppose taxicab arrivals from 3 to 5 p.m. are a Poisson process. If the cabs arrive at an average rate of 18 per hour, what is the probability that a person will have to wait up to 5 minutes for a cab7

Q.12 A random variable takes on values symbolized by x. Jf the available is that normally distributed with a mean of 1000 and a standard deviation of 100 what is the probability that x. will be in the following intervals? (Make a normal curve sketch for each) "" " — ~" i,1000 to 1155 ii. I0S0 toH40 iii.925 to 1075 iv. Less than 865

0.13

Q. I4

0.15

A population consists of five elements 0,2, 4, 5 and 11. Draw ail possible samples of size ! 3 ' . Compute Sample proportion for Even number. Make a sampling distribution of proportion and verify that:

a.

b.

For n = 50, p = 0.01, find from the cumulative tables; n. the binomial probability of fewer than three successes; b. the Poisson probability of fewer than three,successes; c. the difference between the answers to (a) and (b); d. What rule of thumb does the foregoing illustrate?

Explain the following: i. Sample space ii. Class-width iii. Mutually and Non-mutually exclusive events iv. Conditional probability

business statistics

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