Review for Exam 1

Problem 1An inept statistics professor has a home repair project. •With probability 10%, he can buy the necessary equipment at a hardware store and install it properly. This would cost $5.•With probability 60%, he won't be able to fix it himself and will have to call a licensed professional. This would cost $205.•With probability 30%, attempting to fix it himself will only cause additional damage. This would cost $605.

Let X be the amount of money that the project costs. Find E(X) and SD(X).

Problem 2In 48 patients, the amount of a certain drug in the skin (in ng/cm2) is shown in the table below.

3 13 21 24 29 40 4 14 21 25 29 41 4 17 22 26 30 41 7 18 22 26 31 42 7 21 22 26 33 45 8 21 22 26 37 55 9 21 22 27 38 56 9 21 23 28 40 64

Draw a box-and-whisker plot for this data.

Problem 3Draw a histogram for the data in Problem 2.Use the right endpoint convention and the classes

0-20 ng/cm2

20-30 ng/cm2 30-70 ng/cm2

Problem 4Five cards are dealt from a well-shuffled deck. Find the probability that:

a) at least one of them is a heartb) exactly two of them are heartsc) the third card is a heartd) the third card is heart, given that the first two

are spadese) all five cards are hearts

Problem 5

A large data set has mean 62 and standard deviation 14. Fill in the blanks with numbers:

a)About 68% of the data lies between _______ and _______

b)About 95% of the data lies between _______ and _______

Problem 6A box of tickets contains 200 red tickets and 300 green tickets. Ten are selected at random. Find (accurate to four decimal places) the probability that exactly 6 of the tickets are red if …

a)the draws are made with replacementb)the draws are made without replacement

Problem 7In a certain assembly plant has three machines that makes its products.• Machine 1 makes 30% of the products. From past

experience, it is known that 2% of these products are defective.

• Machine 2 makes 45% of the products. From past experience, 3% of these products are defective.

• Machine 3 makes 25% of the products. From past experience, 1% of these products are defective.

Suppose a randomly chosen product is found to be defective. What is the probability that it was made by the third machine?