Gifted/ Accelerated Math 3
Statistics Final Exam Review
1.
Name: _______________________
Date: _______________________
The owner of a large fleet of courier vans is trying to estimate her costs for next year’s operations. A random
sample of 8 vans yields the following fuel consumption data:
10.3 9.7 10.8 12.0 13.4 7.5 8.2 9.1
Calculate the mean and standard deviation of the sample.
Find the probabilities of the following z-scores.
2.
P(z < 1.68)
4.
P( -0.80 < z < -0.15)
3.
P(z > 1.13)
5.
P( 1.21 < z < 1.87)
6.
What is the z-score that corresponds to the 75th percentile?
7.
The mean and standard deviation are $288 and $121.33 respectively for amount of money spent on textbooks.
What’s the probability that one random student will spend $265 or less for books?
8.
The distribution of the heights of students in a large class is roughly bell-shaped. Moreover, the average height is
68 inches, and approximately 95% of the heights are between 62 and 74 inches. Find the standard deviation of
the height distribution.
9.
The Beanstalk Club is limited to women and men who are very tall. The minimum height requirement for women
is 70 inches. Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 in. What percentage of
women could be in the Beanstalk club, meaning they have a height of 70 inches or higher?
10.
On a certain test the mean for the class was 87.5 with a standard deviation of 3.1. If someone made in the top
15% of the class, what grade did they earn on the test?
11.
By 2011 the average household in Georgia owned an average of 4.1 television sets with a standard deviation of
2.3. A simple random sample was taken of 50 households in Augusta and found that they owned an average of
3.4 television sets. What is the probability that any random sample of 50 households would own an average of
3.4 television sets of more?
12.
By 2011 approximately 80% of the population owned a television set. In a group of 100 people chosen at
random, what is the probability that 75 of them or more own a television set?
13.
The National Center for Education Statistics surveyed 4400 college graduates about the lengths of time required
to earn their bachelor's degrees. The mean of the sample is 5.15 years. It is known that the population standard
deviation is 1.68 years. Construct the 95% confidence interval for the mean time required by all college
graduates.
14.
In crash test of 15 Honda Odyssey minivans, collision repair cost are found to have a distribution that is roughly
bell shaped, with a mean of $1786 and a population standard deviation of $937 (based on data from the Highway
Loss Data Institute). Construct the 99% confidence interval for the mean repair cost in all such vehicle collisions.
15.
The mean and standard deviation are $288 and $121.33, respectively, for the amount of money spent on
textbooks at a local university per semester. What is the probability that a student will spend more than $265
for books during the upcoming spring semester? Express your answer to 4 decimal places. Assume the
distribution of money spent forms a normal distribution
16.
The distribution of the heights of students in a large class is approximately normal. Moreover, the average
height is 68 inches with a standard deviation of 4 inches. What percentage of students in the class have a height
between 60 and 76 inches? Please round the percentage to two decimal places.
17.
In Mrs. Whitmire’s Math 1 class, the grades on the Statistics' test follow a normal distribution, with the average
grade being 87.5 and a standard deviation of 3.1. If a student scored better than 65% of their classmates, what
score did he/she make on the test? Please round your answer to the nearest whole number.
18.
The National Center for Education Statistics surveyed 40 college graduates about the lengths of time required to
earn their bachelor's degrees. The mean of the sample is 5.15 years. It is known that it takes all college
graduates a mean time of 5.75 years with a standard deviation is 1.68 years to earn their bachelor's degrees. If
the population is normal, what is the probability that it takes a sample of 40 college graduates 5.15 or more years
to complete their bachelor’s degree? Express to four decimal places.
19.
A USA Today poll asked a random sample of 1012 U.S. adults what they did with their cereal milk after they have
eaten the cereal. Of the respondents, 67% said that they drink the milk. Suppose we know that 70% of all U.S.
adults drink the cereal milk. What is the probability that a random sample of this size would have the response
rate of 67% or less to the question? Express your answer to four decimal places.
20.
A hotel chain wanted to learn about the level of experience of its general managers. A random sample of 14
general managers was selected, and these managers had a mean of 11.72 years of experience. Suppose that the
standard deviation of years of experience for all general managers in the chain is known to be 3.2 years. What is
the 95% confidence interval for the mean experience of all general managers in this hotel chain? Please round
all numbers to two decimal places.
21.
It is not known what percentage of all adults in Ohio support an increase in the state sales tax from 5% to 6%,
with the additional revenue going to education. A survey asks a random sample of 123 adults in Ohio if they
support the tax increase, and it finds that 45 of them agree with the state sales tax increase from 5% to 6%.
Construct a 99% confidence interval for the percentage of all adults in Ohio that support an increase in state
sales tax. Please round the percentage to two decimal places.
Answers:
11.
0.9842
1.
X-bar = 10.125;
12.
0.8944
standard deviation of the sample = 1.95
13.
[5.10, 5.2]
2.
0.9535
14.
[$1162.78, $2409.22]
3.
0.1292
15.
0.5753
4.
0.2285
16.
95.44%
5.
0.0824
17.
89
6.
0.67 or 0.68
18.
0.9881
7.
OMIT
19.
0.0188
8.
3
20.
[10.04, 13.40]
9.
0.52%
21.
[25.40%, 47.78%]
10.
90.72%