Midterm exam part 2

Midterm Exam (Part 2)

There are six (6) total questions over two (2) pages.

Part 2 is worth sixty (60) total points.

Please ensure that you have also completed the multiple choice portion (Part 1) of this exam.

Name: _____________________________________________

Answer the following six (6) questions. Show all work. Partial credit may be awarded.

1. The finishing process on new furniture leaves slight blemishes. The table below displays a manager's probability assessment of the number of blemishes on one piece of new furniture.
(10 points.)

Number of Blemishes	0	1	2	3	4	5
Probability	0.34	0.25	0.19	0.11	0.07	0.04

A) On average, how many blemishes do we expect on one piece of new furniture?

B) What is the standard deviation of blemishes on one piece of new furniture?

2. The probability that a person catches a cold during the cold-and-flu season is 0.4. Assume that 10 people are chosen at random. (10 points.)

A) On average, how many of these ten people would you expect to catch a cold?

B) What is the standard deviation of the number of people who catch a cold?

3. The number of nails in a five-pound box is normally distributed with a mean of 563.3 and a standard deviation of 33.2. (10 points.)

A) What is the probability that there are less than 500 nails in a randomly-selected five-pound box of nails?

B) The probability is 0.99 that a randomly-selected five-pound box of nails contains at least how many nails approximately?

4. You are the owner of a small casino in Las Vegas and you would like to reward the high-rollers who come to your casino. In particular, you want to give free accommodations to no more than 10% of your patrons. Suppose that the amount wagered by patrons follows a normal distribution. The mean amount wagered by all patrons is $287 with a standard deviation of $15. You should give free accommodations to those individuals who wager over how much money?
(5 points.)

5. Candidates for employment at a city fire department are required to take a written aptitude test. Scores on this test are normally distributed with a mean of 260 and a standard deviation of 51.
A random sample of nine (9) test scores is taken. (10 points.)

A) What are the mean and standard error of the sample mean scores?

B) What is the probability that the sample mean score is less than 250?

6. It has been found that 62.1% of all unsolicited third-class mail delivered to households goes unread. Over the course of a month, a household receives 100 pieces of unsolicited mail.
(15 points.)

A) What is the mean of the sample proportion of pieces of unread mail?

B) What is the standard error of the sample proportion?

C) What is the probability that the sample proportion is greater than 0.60?