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 coldandflu 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 fivepound
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 randomlyselected fivepound box of nails?
B)
The probability is 0.99 that a
randomlyselected fivepound 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 highrollers 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 thirdclass 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?