Download Statistics Name___________________________ Chapter 8

Statistics
Name___________________________
Chapter 8 Review
Period____ Date__________________
1. Sandra wants to study the allocation of government money to universities to be used for
scientific research. She has taken a random sample of 60 universities and recorded the amount
each university received in federal government grants for scientific research. The data has a
mound-shaped histogram but does not appear to follow a normal distribution.
(a) Is it reasonable for her to use the normal distribution to approximate the distribution of
individual grant amounts? Give a reason for your answer.
(b) Could she use the normal distribution to study the distribution of sample means for random
samples of 50 university grant amounts? Explain.
2. Carl is doing a project for his ecology class. He read that the average person uses about 100
gallons of water per day. He estimates the standard deviation to be about 30 gallons per day.
(a) Assuming that Carl’s figures are correct, find the probability that a random sample of 49
people will have a sample mean water use of 90 gallons per day or less.
(b) Find the probability that a random sample of 64 people will have a sample mean water use
over 110 gallons per day.
Statistics
Name___________________________
Chapter 8 Review
Period____ Date__________________
3. Hank has a hot dog stand across the street from a little league ball field. He has observed that the
daily demand for hot dogs on a weekend follows a normal distribution with mean  = 400 and
standard deviation  = 50.
(a) Find the probability that the demand for hot dogs on a weekend day chosen at random will be
less than 300.
(b) Find the probability that the sample mean demand for a random sample of 4 weekend days
will be less than 300.
(c) Compare your answers to parts (a) and (b). Explain the difference.
4. Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a
long train. The automatic hopper car loader is set to put 85 tons of coal into each car. The actual
weights of coal loaded into each car is normally distributed with mean µ = 85 tons and standard
deviation  = 2 tons.
(a) What is the probability that one car chosen at random will have less than 83 tons of coal?
(b) What is the probability that five cars chosen at random will have a mean load weight x
less than 83 tons of coal?
of
Statistics
Name___________________________
Chapter 8 Review
Period____ Date__________________
5. The dean of a liberal arts school claims that the average weekly income of graduates of her
school one year after graduation is $480. Assume that the dean’s claim is correct. Given that the
distribution of weekly incomes has a standard deviation of 160, what is the probability that 40
randomly selected graduates have an average weekly income of less than $450? Round answer to
nearest ten-thousandth.
6. Suppose you know that the x distribution has a mean of   77 and a standard deviation of
  16, but you do not know if the distribution is normal. You draw samples of size 42 from the x
distribution. Let x represent the sample mean. Is the sample size large enough? If so, how could
you standardize the x distribution?
7. The manager of a chocolate factory has observed that the number of chocolates in each
“43-ounce” box is actually a normally distributed random variable, with a mean of 43.6 ounces and
a standard deviation of 0.8 ounces. Find the probability that if a customer buys one box of
chocolates the box will contain more than 43 ounces.
Statistics
Name___________________________
Chapter 8 Review
Period____ Date__________________
Answers
Reference: [8.1.17]
[1]
(a) No, the distribution of individual grant amounts may not be approximately normal.
(b) Yes, for a variable with a mound-shaped distribution, sample means for samples of size 50
will have a distribution which is approximately normal.
Reference: [8.1.26]
[2]
(a) For n = 49, P( x  90) = 0.0099
(b) For n = 64, P( x > 110) = 0.0038
Reference: [8.1.43]
[3]
(a) P(x < 300) = 0.0228
(b) P( x < 300) = 0.0001
(c) The probability for part (b) is smaller because the standard deviation is smaller and the values
of x tend to be closer to the mean.
Reference: [8.1.52]
[4]
(a) 0.1587
(b) 0.0122 I got .0125
Reference: [8.2.2.78]
[5] 0.5753 I got .1170. Problem is different in book.
Reference: [8.2.2.80]
x  77
[6] Yes; z 
2.5
Reference: [8.2.2.81]
[7] 0.7734