Pre-Calculus
Chapter 11 Test Review
Name _______________________________ Pd ____
9. The enrollment for a biannual computer camp over the past 15 years is shown.
Number of Participants
45, 68, 55, 25, 48, 36, 61, 52, 31, 8, 41, 58, 40, 55, 68,
47, 60, 28, 44, 63, 18, 68, 50, 57, 37, 16, 56, 40, 50, 68
a) Construct a histogram and a box plot for the given set of data.
b) Describe the distribution of the data using the appropriate statistics.
10. Participants in a punt, pass, and kick competition achieved the following distances for the punt portion of the
competition.
Distances (feet)
46, 90, 62, 78, 70, 64, 47, 56, 76, 61, 83, 65, 74, 50, 63, 80, 60, 47, 33, 75, 60, 34, 44, 54, 67, 53, 57, 29
a) Construct a histogram and a box plot for the given set of data.
b) Describe the distribution of the data using the appropriate statistics.
11. Elisa recorded the amount of time in minutes that she spent waiting in lines for rides at an amusement park.
Time (minutes)
64, 5, 48, 10, 22, 89, 12, 28, 2, 14, 35, 1, 17, 12, 85, 32, 16, 42, 56, 20, 11, 21, 16, 25, 4, 34
a) Construct a histogram and a box plot for the given set of data.
b) Describe the distribution of the data using the appropriate statistics.
12. The monthly low temperatures for two cities are shown.
Astoria, OR
36, 51, 37, 42, 54, 39, 53,
42, 46, 38, 50, 47
Boston, MA
22, 57, 46, 24, 31, 41, 64,
50, 28, 59, 65, 38
a) Construct side-by-side box plots of the data sets.
b) What do the box plots reveal about the average annual low temperature for each city?
c) What do the box plots reveal about the temperature variation for each city throughout the year?
13. The attendance for a sample of the home owners’ association meetings for two neighboring communities is
shown.
Chase Meadows
Eaton Estates
42, 94, 100, 40, 76, 23, 60, 96, 68,
72, 58, 45, 62, 80, 48
132, 179, 115, 56, 137, 112, 85,
145, 92, 108, 128, 185, 45, 80, 168
a) Construct side-by-side box plots of the data sets.
b) Which community has a higher attendance to home owners’ association meetings, on average?
c) Which community has a greater variation in attendance to home owners’ association meetings?
14. The manager of a kennel records the weights for a sample of dogs currently being housed.
Weight (pounds)
31, 67, 8, 37, 12, 87, 14, 34, 105, 57, 42, 8, 16, 54, 17, 20, 72,
23, 27, 63, 24, 52, 14, 44, 27, 5, 28, 22, 33, 15, 6, 36, 41, 21, 46
a) What is the mean of the weights?
b) What is the median of the weights?
c) If each dog gains 5 pounds, how will the mean and median be affected?
15. The speeds, in miles per hour, of 24 cars on a particular road are recorded and represented on the box-andwhisker plot shown below. Answer each of the following questions based on this diagram.
a) Describe the set of data using the 5-number summary.
b) What is the range of this data set?
c) What is the maximum speed of the 24 drivers?
d) How many drivers drove between 53 and 71 mph?
e) If the speed limit on this part of the road is 70 miles per hour, are more people speeding or are more going
below the speed limit? Justify.
16. Match each histogram with the appropriate box plot.
1.
_______
2.
_______
A.
B.
3.
_______
4.
_______
C.
D.
5.
_______
E.
17. The table gives the frequency distribution of the inauguration ages of all of the presidents.
Age at
Inauguration
Frequency
40-45
2
45-50
8
50-55
16
55-60
9
60-65
7
65-70
2
a) Construct a percentile graph of the data.
b) Approximately what percentage of the presidents were inaugurated at age 55 or younger?
c) Approximately what president age corresponds to the 20th percentile?
d) Approximately what president age corresponds to Q3?
e) What is the median president age?
18. In a normal distribution, what percent of the values lie…
a. Below the mean?
b. Above the mean?
c. Within 1 standard deviation of the mean?
d. Within 2 standard deviations of the mean?
e. Within 3 standard deviations of the mean?
19. The mean life of a tire is 30,000 km. The standard deviation is 2000 km.
a. Use the mean and standard deviation to label 1, 2, and 3 standard deviations from the mean on the
following normal distribution graph.
b. 68% of all tires will have a life between _________ km and _________ km.
c. 95% of all tires will have a life between _________ km and _________ km.
d. What percent of the tires will have a life that exceeds 26,000 km?
e. If a company purchased 2000 tires, how many tires would you expect to last more than 28 000 km?
20. A line up for tickets to a local concert had an average waiting time of 20 minutes with a standard deviation of 4
minutes.
a. What percentage of the people in line waited for more than 28 minutes?
b.
If 2000 ticket buyers were in line, how many of them would expect to wait for less than 16 minutes?
21. The average time it takes runners to complete a 10K is normally distributed with a mean of
63.3 minutes and a standard deviation of 12.3 minutes.
a. About what percent of the runners take more than 80 minutes to complete the 10K?
b. About what percent of the runners take between 50 and 60 minutes?
c. About what percent of the runners take less than 40 minutes to complete the 10K?
d. Participants whose times fall in the top 10% of the distribution are given a medal. What time does a
runner need to get to receive a medal?
22. The weights of adult male greyhound dogs are normally distributed. The mean weight is about 68.3 pounds and
the standard deviation is about 8.6 pounds.
a. Approximately what percent of adult male greyhound dogs would you expect weigh between 60 and 70
pounds?
b. What would you expect an adult male greyhound dog to weigh if it weighed in the 90th percentile of all
adult greyhounds?
c. What would you expect an adult male greyhound dog to weight if it weighed in the 50th percentile of all
adult greyhounds?
d. What range of weights do the middle 50% of adult male greyhound dogs have?
23. A poll of 388 randomly chosen office workers showed that they spend an average of 1.8 hours not working
while on the clock. The standard deviation is 0.6 hour. Determine a 90% confidence interval for the population
mean. Then, describe what the interval means in a sentence.
24. A sample of 400 adults was asked the average time spent watching television each weeknight. The mean time
was 68.4 minutes with a standard deviation of 20.9 minutes. Determine a 95% confidence interval for the
population mean. Then, describe what the interval means in a sentence.
25. A marketing manager wants to create an advertisement for a new phone stating that the user can surf the
Internet for at least 24 consecutive hours before the battery needs to be recharged. The quality control
department tests a sample of 163 phones and calculates a mean time of 23.6 hours before the battery needs
recharged. The standard deviation is 1.2 hours. Test the hypothesis at 5% significance.
26. A sales manager claims that her representatives spend no more than 5 minutes with each of their customers.
Using a sample of 132 customers, the manager calculated a mean duration of 5.1 minutes and a standard
deviation of 0.6 minute. Test the hypothesis at 1% significance.
27. Kim is a quality tester for a tropical fruit company. The company claims that their canned pineapple stays fresh
for at least 16 hours after opening. Kim tests 15 different cans to see if they actually stay fresh for at least 16
hours.
12
12
14
14
12
11
Number of Hours Each Can Stays Fresh
7
12
13
16
17
18
10
9
6
a. Construct a histogram and a box plot for the given set of data.
b. Describe the distribution of the data using the appropriate statistics.
c. Assume that the data is distributed normally. What percent of the distribution stays fresh for at least 16
hours?
d. Find the 95% confidence interval of the pineapple cans made by the tropical fruit company. Then,
describe what the interval means in a sentence.
e. Determine whether there is enough evidence to reject the claim at 5% significance.
28. Miss Henry is a high school math teacher at Northwestern High School. She claims that the average weight of
the back packs carried by the students at her school is 18 pounds. Miss Henry weighs 30 random back packs to
determine if her claim is supported. The weights are shown below.
a. Construct a histogram and a box plot for the given set of data.
b. Describe the distribution of the data using the appropriate statistics.
c. Assume that the data is distributed normally. What percent of the back packs weighs less than 18
pounds?
d. Find the 90% confidence interval of the student back pack weights. Then, describe what the interval
means in a sentence.
e. Determine whether there is enough evidence to reject the claim at 10% significance.