EMGT 571: Statistics I Take Home Final Exam

EMGT 571
STATISTICS I
TAKE HOME FINAL EXAM

Problems – Answer the following problems…BE SURE TO SHOW ALL WORK!!!. You can use excel, SPSS or word as the medium for generating solutions to the problems. I recommend you use excel and SPSS

1. The time at which the mailman delivers the mail follows a normal distribution with a mean of 2:00PM and a standard deviation of 15 minutes (20 pts)

a) What is the probability that the mail will arrive before 1:50PM? b) What is the probability that the mail will arrive after 2:30PM? c) What is the probability that the mail will arrive between 1:40PM and 2:20PM? d) Between what two times (equally before the mean and equally after the mean) accounts for the mail being delivered 95% of the time?

2. The income of junior executives in a large corporation are normally distributed with a standard deviation of $1200. A cutback is pending, at which time those who earn less than $28,000 will be discharged. If such a cut represents 10% of the junior executives, what is the current mean (average) salary of the group of junior executives? (10 points)

3. A large industrial firm uses 3 local motels to provide overnight accommodations for its clients. From past experience it is known that 20% of the clients are assigned rooms at the
Ramada Inn, 50% at the Sheraton, and 30% at the Holiday Inn. It is found (a given condition) that plumbing is faulty at 5% of the rooms at the Ramada Inn, 4% of the rooms at the Sheraton, and 8% of the rooms at the Holiday Inn. What is the probability that: (10 pts)

a) A client will be assigned a room with faulty plumbing b) A person with a room having faulty plumbing was assigned accommodations at the Holiday Inn

4. Suppose that four inspectors at a film factory are suppose to stamp the expiration date on each package of film at the end of the assembly line. John, who stamps 20% of the packages, fails to stamp the expiration date once in every 200 packages. Tom, who stamps 60% of the packages, fails to stamp the expiration date once in every 100 packages. Jeff, who stamps 15% of the packages, fails to stamp the expiration date once in every 90 packages. And, Pat, who stamps the remaining packages, fails to stamp the expiration date once in every 200 packages. If a customer complains that her package of film does not show the expiration date, what is the probability that it was inspected by John? (10 pts) 5.
A manufacturer of a certain type of large machine wishes to buy rivets from one of two suppliers. It is important that the breaking strength of each rivet exceed 10,000 PSI. (Below 10,000 PSI results a defective rivet). Two suppliers (A & B) offer this type of rivet. Both have rivets whose breaking strength are normally distributed. The mean breaking strength of supplier A is 14,000 PSI with a standard deviation of 2,000 PSI. The mean breaking strength of supplier B is 13,000 PSI with a standard deviation of 1,000 PSI. Which supplier should the manufacturer go with? Why? (Hint: think about the “amount of defects” that result from each supplier) (10
pts)

6. A candy company distributes boxes of chocolates with a mixture of creams, toffees and cordials. Suppose that the weight of each box is 1 kilogram, but the individual weights of the creams, toffees and cordials vary from box to box. For a randomly selected box, let X = weight of creams and Y =weights of the toffees and the pdf is described as: (20 pts) f(x,y)= 0 elsewhere

a. Find the probability that in a given box, the cordials amount for more than half of the weight b. Find the marginal density for the weight of the creams c. Find the probability that the weight of the toffees in a box of less than 1/8 of a kilogram given that creams constitute ¾ of the weight

7. Three cards are drawn without replacement from the 12 face cards (jacks, queens and kings) of an ordinary deck of 52 playing cards. Let X be the number of kings selected and Y the number of jacks selected. Find: (10 pts)

a. The joint probability distribution function (show in a joint probability table) b. The probability of getting 2 jacks and 1 king c. The probability of getting 1 jack, regardless of the number of kings d. The probability of getting a jack and a queen given 1 king is selected