8/13/2019 DIT2010fall002

1/3

Villanova UniversityCollege of Commerce and Finance

Department of Decision and Information Technologies

DIT2010 Fall, 2000Eam II E! "e#ster

$lease sho% all of yo&r %or' for credit!

1! "e#ster (ssociates reports that the mean clear height for a Class ( %areho&se in theUnited )tates is 22 feet! )&ppose clear heights are normally distri#&ted and that thestandard deviation is * feet! ( Class ( %areho&se in the United )tates is randomlyselected!

a! "hat is the pro#a#ility that the clear height is #et%een 2+ and 1 feet- (8 points)

#! )&ppose the mean clear height of all U!)! Class ( %areho&ses is &n'no%n #&t thestandard deviation is 'no%n to #e * feet! "hat is the val&e of the mean clearheight if 2./ of U!)! class ( %areho&ses have a clear height less than 20 feet- (7points)

2! &ality Foods regional manager %ants to determine the average fat content per pond ofstea' sold in $ortland, aine! )hes considering 3&itting her 4o# and starting a cattleranch after reading the article 5&een of the 6ange7 in the 8an&ary iss&e of SuccessfulFarming! 9er ranch %o&ld prod&ce lo%:fat #eef for sale to &pscale cons&mers! )hep&rchased one stea' from each of the 1; stores in the area and determined the fat content

per po&nd! The pop&lation standard deviation of all fat content is 'no%n to #e 0!0o&nces! The data

1!2 1!

1!? 1!

1! 1!?

!@ 1!1

1! 1!2

1!@ 1!

!. !.

1!; 1!*

1! 1!*

a! (ss&ming that the fat content is normally distri#&ted, calc&late a .+/ confidenceinterval for the average fat content per po&nd in stea's sold in the $ortland, aine,area! (10 points)

8/13/2019 DIT2010fall002

2/3

#! 9er research sho%s that the stea's from her ranch %ill average 1!0 oA of fat perpo&nd! (re her stea's significantly lo%er in fat content than the ones availa#le in the$ortland area- Eplain %hy or %hy not statistically! (5points)

! )&ppose a sdivision on the so&th%est side of $hiladelphia contains 1+00 ho&ses! Themean appraised val&e of a ho&se in this sdivision for all ho&ses is B1*@,000, %ith astandard deviation of B;+00! ( sample of 100 ho&ses is selected randomly and eval&ated#y an appraiser!

a! "hat is the pro#a#ility that the sample average is greater than B1*.,000- (10points)

#! "hat ass&mption m&st #e made in order to solve $art a- Can this ass&mption #e

made and %hy- (5 points)

*! (ccording to the (ir Transport (ssociation of (merica, the average operating cost of anD:;0 4et airliner is B20;@ per ho&r! )&ppose the operating costs of an D:;0 4etairliner are normally distri#&ted %ith a standard deviation of B1@+ per ho&r! For %hatoperating cost %o&ld only 20/ of the operating costs #e less- (8 points)

+! ( large am&sement par' has recently added + ne% rides, incl&ding a large roller coastercalled the ind Eraser! anagement is concerned a#o&t the %aiting times on the ne%roller coaster! ( random sample of 10 people is selected and the time

Mind Eraser

* ??

;0 +*

*; @2

?1 +;

@* ?;

a! Find a .0/ confidence interval for the average %aiting time for the ind Eraser,ass&ming that the %aiting time is normally distri#&ted!

8/13/2019 DIT2010fall002

3/3