Business Statistics

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DEPARTMENT OF FINANCE AND OPERATIONS

FACULTY OF MANAGEMENT

STAT-2066EL-01/02: Business Statistics – Fall 2019

Assignment 2

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Instructions

 This assignment is to be done individually or groups of two students.

 Due date: Thursday November 14, 2019 (in class)

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Problem 1. (10 marks in total) In order for you to become a member of Mensa, a worldwide

organization with approximately 100,000 members, your IQ must be in the top 2%. The word

mensa is Latin for “table,” and was chosen to denote a group or round table of people with equal

ability. In 1996, Mensa, which was founded by two British barristers, celebrated its 50th birthday.

American Mensa Ltd., which was founded in 1960 has almost 50,000 members. Marilyn vos

Savant, who is reputed to have the highest registered IQ, is a member. Assuming that IQ scores

have an approximately normal distribution with a mean and standard deviation of 100 and 15,

respectively, answer the following questions.

a. (3 marks) What IQ must one have in order to become a member of Mensa?

b. (2 marks) What percent of all Americans have an IQ of at least 145?

c. (2 marks) What percent of all members of Mensa have an IQ of at least 145?

d. (3 marks) If Mensa decided to become more exclusive, and accepted only the top 1%

instead of the top 2% as members, what IQ would one need in order to become a member

of Mensa?

Problem 2. (11 marks in total) A business convention holds its registration on Wednesday

morning from 9 A.M. until 12 noon. History has shown that registrant arrivals follow a Poisson

distribution at an average rate of 1.8 every 15 seconds. Fortunately, several facilities are

available to register convention members.

a. (2 marks) What is the average number of seconds between arrivals to the registration area

for this convention based on past results?

b. (3 marks) What is the probability that 25 seconds or more would pass between

registration arrivals?

c. (3 marks) What is the probability that less than 5 seconds will elapse between arrivals?

d. (3 marks) Suppose the registration computer went down for a 1-minute period. Would

this condition pose a problem? What is the probability that at least 1 minute will elapse

between arrivals?

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Problem 3. (5 marks) A College food services buys frozen fish in boxes labeled 10 pounds. The

true average weight of the boxes is 8 pounds with a standard deviation of 2 pounds. The food

service director suspects that the boxes do not contain as much fish as advertised. He decides to

inspect 40 boxes from the next shipment. If the average weight is less than 10 pounds, he will

reject the entire shipment. Find the probability that the food service director will not reject the

shipment.

Problem 4. (19 marks) Consider the following function:

0 5 25

( ) 10

5 10 25

x x

f x x

x

  

    



a. (3 marks) Graph ( )f x .

b. (4 marks) Is ( )f x a probability density function? Why?

c. (3 marks) What is the probability that X lies between 1 and 3?

d. (3 marks) What the probability that X lies between 4 and 8?

e. (3 marks) What is the probability that X is less than 7?

f. (3 marks) What is the probability that X is greater than 3.

Acknowledgments

Problem 1 is from “Discovering Statistics and Data”, by James S. Hawkes. Problem 2 is from

“Business Statistics for Contemporary Decision Making”, by Ken Black, Chuck Chakrapani, and

Ignacio Castillo. Problem 3 is from “Discovering Business Statistics”, by Quinton J.

Nottinghman, and James S. Hawkes