# Statistics I Final Exam

**Topics:**Normal distribution, Standard deviation, Arithmetic mean

**Pages:**3 (778 words)

**Published:**May 1, 2011

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...

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