Download Lauren is enrolled in a very large college calculus class

Multiple Choice Questions Ch. 8
AP STATS
Name________________
Date_______Per______
For sample means:
z
statistic-parameter
standard deviation
x 

n
For sample proportions:
p(1  p)
 pˆ 
n
Problems where you have to use Z-scores:
1.
Lauren is enrolled in a very large college calculus class. On the first exam, the class mean was 75 and the standard
deviation was 10. On the second exam, the class mean was 70 and the standard deviation was 15. Lauren scored
85 on both exams. Assuming the scores on each exam were approximately normally distributed, on which exam
did Lauren score better relative to the rest of the class?
A She scored much better on the first exam.
B She scored much better on the second exam.
C She scored about equally well on both exams.
D It is impossible to tell because the class size was not given.
E
2.
It is impossible to tell because the correlation between the two sets of exam scores is not given.
The weights of a population of adult male gray whales are approximately normally distributed with a mean weight
of 18,000 kilograms and a standard deviation of 4,000 kilograms. The weights of a population of adult male
humpback whales are approximately normally distributed with a mean weight of 30,000 kilograms and a standard
deviation of 6,000 kilograms. A certain adult male gray whale weighs 24,000 kilograms. This whale would have
the same standardized weight (z-score) as an adult male humpback whale whose weight, in kilograms, is equal to
which of the following?
A 21,000 B 24,000
3.
D 36,000
E 39,000
Suppose that a Normal model describes fuel economy (mpg) for automobiles and that a Toyota has a standardized
score (z-score) of +2.2. This mean that Toyotas….
A get 2.2 miles per gallon.
B get 2.2 times the gas mileage of the average car.
C get 2.2 mpg more than the average car.
D have a standard deviation of 2.2 mpg.
E
4.
C 30,000
achieve fuel economy that is 2.2 standard deviations better than the average car.
Golf balls must meet a set of five standards in order to be used in professional tournaments. One of these standards
is distance traveled. When a ball is hit by a mechanical device, Iron Byron, the distance the ball travels may not
exceed 291.2 yards. Manufacturers want to develop balls that will travel as close to the 291.2 yards as possible
without exceeding that distance. A particular manufacturer has determined that the distances traveled for the balls
it produces are normally distributed with a standard deviation of 2.8 yards and a mean of 288 yards. Which of the
following represents the probability that a ball randomly selected will travel too far?
A
D
288  291.2 

P z 

2.8


P  x  288
291.2  288 

B P z 

2.8


E P  x  291.2 
291.2  288 

C P z 

2.8


5.
Gina’s doctor told her that the standardized score for her systolic blood pressure, as compared to the blood pressure
of other women her age, is 1.50. Which of the following is the best interpretation of this standardized score?
A Gina’s systolic blood pressure is 150.
B
Gina’s systolic blood pressure is 1.50 times the average systolic blood pressure of women her age.
C Gina’s systolic blood pressure is 1.50 above the average systolic blood pressure of women her age.
D Gina’s systolic blood pressure is 1.50 standard deviations above the average systolic blood pressure of women
her age.
E Only 1.5% of women Gina’s age have a higher systolic blood pressure than she does.
6.
Golf courses have a wide range of difficulty. Similarily, players differ in ability. In order to adjust for variations
between players, they are often assigned a handicap score. To adjust for variations between courses, a handicapper
decides to compare the golfer’s score against the data from the course. Suppose that course A plays at a mean
score of 76 with a standard deviation of 8 strokes with an approximately normal distribution of scores. The mean
score for course B is 80 with a standard deviation of 6 strokes and the scores are also approximately normally
distributed. If a golfer regularly shoots an 80 on course A, what should be the comparable score on course B?
A 80
7.
B 83
C 84
D 86
E 88
According to the US Census, the proportion of adults in a certain county who owned their home was 0.71. An SRS
of 100 adults in a certain section of the county found 65 owned their home. Which one of the following represents
the approximate probability of obtaining a sample of 100 adults in which fewer than 65 own their home, assuming
that this section of the county has the same overall proportion of adults who own their home as does the entire
county?
A
C
100 
65
35

 .71 .29 
 65 


0.65  0.71
P z 

 0.71 0.29 

100

100 
65
35
 .29  .71
 65 
B









0.65  0.71 
D P z 
 0.65  0.35  



100





0.65  0.71 
E P z 
 0.71 0.29  



100


8.
The distribution of the heights of students in a large class is roughly Normal with a mean of 68 inches.
Approximately 95% of the heights are between 62 and 74 inches. What is the standard deviation of the height
distribution?
B3
C6
D9
E 12
A 2
9.
The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard
deviation of 2 inches. If Rachael is at the 99th percentile in height for adult women, then her height, in inches, is
closest to
B 62
C 68
D 70
E 74
A 60
Regular Multiple Choice Problems:
10. Suppose that 11.5-ounce package of chocolate chip cookies are produced with weights that follow a Normal
distribution with mean weight 11.6 ounces and standard deviation 0.05 ounce. Approximately what percent of the
bags will likely be underweight (that is, less than 11.5 ounces)?
A 2.5%
B 5%
C 16%
D 32%
E 64%
11. Let X represent a variable whose distribution is normal, with a mean of 100 and a standard deviation of 10. Which
of the following is equivalent to P  X  115 ?
A
12.
P  X  115
C P  X  85
B 0.46
C0.00248
D 0.005
E
D 72% is a parameter and 56% is a statistic
72% and 56% are both parameters
A survey asks a random sample of 1500 adults in Ohio if they support an increase in the state sales tax from 5% to
6%, with the additional revenue going to education. Let p̂ denote the proportion in the sample who say they
support the increase. Suppose that 40% of all adults in Ohio support the increase. The standard deviation of p̂ is
A 0.40
B 0.24
C 0.0126
D 0.00016
E0
A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27. The true
population proportion of American teenagers who have a cell phone is 0.29. For samples of size 1,000 that are
selected at random from this population, what are the mean and standard deviation, respectively, for the sampling
distribution of the sample proportion of American teenagers who have a cell phone?
A
 0.27  0.73
 0.29  0.71
B 0.27,
C 0.27,
0.27, 1000  0.27  0.73
1000
D
0.29,
16.
E None of the above
B 72% and 56% are both statistics
C 72% is a statistic and 56% is a parameter
15.
E 1  P  X  85
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had
voted in the election. Election records show that only 56% of registered voters voted in the election. Which of the
following statements is true about the boldface numbers?
A 72% is a sample; 56% is a population
14.
D P  85  X  115
In a large population, 46% of the households own VCRs. A simple random sample of 100 households is to be
contacted and the sample proportion computed. What is the standard deviation of the sampling distribution of the
sample proportion?
A 46
13.
B P  X  85
 0.29  0.71
1000
1000
E 0.29, 1000  0.29 0.71
In a large population of adults, the mean IQ is 112 with a standard deviation of 20. Suppose 200 adults are
randomly selected for a market research campaign. The distribution of the sample mean IQ is
A exactly Normal, mean 112, standard deviation 20.
B
approximately Normal, mean 112, standard deviation 0.1.
C approximately Normal, mean 112, standard deviation 1.414.
D approximately Normal, mean 112, standard deviation 20.
17. A certain type of remote-control car has a fully charged battery at the time of purchase. The distribution of running
times of cars of this type, before they require recharging of the battery for the first time after its period of initial use,
is approximately normal with a mean of 80 minutes and a standard deviation of 2.5 minutes. The area shaded in the
figure below represents which of the following probabilities?
A
The probability that the running time of a randomly selected car of this type, before it requires recharging of
the battery for the first time after its period of initial use, is between 75 minutes and 82.5 minutes.
B
The probability that the running time of a randomly selected car of this type, before it requires recharging of
the battery for the first time after its period of initial use, is between 75 minutes and 85 minutes.
C
The probability that the running time of a randomly selected car of this type, before it requires recharging of
the battery for the first time after its period of initial use, is between 77.5 minutes and 82.5 minutes.
D
The probability that the running time of a randomly selected car of this type, before it requires recharging of
the battery for the first time after its period of initial use, is between 77.5 minutes and 85 minutes.
E
The probability that the running time of a randomly selected car of this type, before it requires recharging of
the battery for the first time after its period of initial use, is between 77.5 minutes and 87.5 minutes.
18. It has been estimated that as many as 70% of the fish caught in certain areas of the Great Lakes have liver cancer
due to the pollutants present. A sample of 130 fish is caught and inspected for signs of liver cancer. The number
of infected fish within two standard deviations of the mean is
A (81, 101).
B (86, 97).
C (63, 119).
D (36, 146).
E (75, 107).
19. Seventeen people have been exposed to a particular disease. Each one independently has a 40% chance of
contracting the disease. A hospital has the capacity to handle 10 cases of the disease. What is the probability that
the hospital’s capacity will be exceeded?
A 0.965
B 0.035
C 0.989
D 0.011
E 0.736
20. Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X
is Normal with mean $360 and standard deviation $50. What is the value of
P(X > $400)?
A 0.2119
B 0.2881
C 0.7881
E The answer cannot be computed from the information given.
D 0.8450
21. A recent study was conducted to investigate the duration of time required to complete a certain manual dexterity
task. The reported mean was 10.2 seconds with a standard deviation of 16.0 seconds. Suppose the reported values
are the true mean and standard deviation for the population of subjects in the study. If a random sample of 16
subjects is selected from the population, what is the approximate probability that the mean of the sample will be
more than 11.0 seconds?
B 0.4800
C 0.5793
D 0.5200
A 0.4207
E
It cannot be concluded that the population distribution is normal and therefore the probability cannot be calculated.
1. C 2. E 3. E 4. B 5. D 6. B 7. C 8. B 9. D 10. A 11. C
12. E 13. C 14.C 15. D 16. C 17. A 18. A 19. B 20. A 21. E