Download Sample Questions Mastery #4

Sample Questions Mastery #4
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. If X~N(10, 32), then the standard deviation equals
a. 10
c. 3
b. 9
d. 1
____
2. If X~N( 2, 22), then equals
a. 2
c. 2
b. 0
d. 4
2
3. If X~N(15, 2 ), then 68% of the data fall in the interval
a. 9–21
c. 13–17
b. 11–19
d. 15–17
____
____
____
____
____
____
____
____
____
4. If X~N
a. 34%
b. 47.5%
, what percent of the data fall between and
c. 50%
d. 95%
?
5. If X~N(12.4, ) and 95% of the data lie in the interval 11.8–13.0 the equals
a. 1.2
c. 0.09
b. 0.3
d. 0.06
6. Annual rainfall in Coastville is normally distributed with a mean of 60 cm and a standard deviation of 7 cm.
For what percent of the years will the annual rainfall be between 53 cm and 60 cm?
a. 5%
c. 34%
b. 16%
d. 68%
7. IQ is normally distributed with a mean of 100 and a standard deviation of 15. What percent of the population
has an IQ less than 55?
a. 0%
c. 0.3%
b. 0.15%
d. 5%
8. The masses of 500 boxes of sugar are approximately normally distributed with a mean of 150g and a standard
deviation of 3g. How many of these boxes would you expect to have a mass greater than 150g?
a. 250
c. 256
b. 253
d. 259
9. The nicotine content in a certain brand of cigarettes has a normal distribution with a mean of 1.5 mg and a
standard deviation of 0.2 mg. What percent of these cigarettes have a nicotine content less than 0.7 mg?
a. 5%
c. 0.15%
b. 0.3%
d. less than 0.15%
10. Suppose that masses of newborn children are normally distributed with a mean of 3.4 kg and a standard
deviation of 0.8 kg. A newborn is potentially at risk if the baby’s mass falls in the lowest 2.5%. These babies
have a mass less than
a. 3.4 kg
c. 1.8 kg
b. 2.6 kg
d. 1.0 kg
11. The variable has a normal distribution with 99.7% of the area under its curve falling symmetrically between x
= 50 and x = 170. Its mean and standard deviation are respectively
a. 110 and 20
c. 120 and 20
b. 110 and 202
d. 120 and 202
____ 12. Diameters of ball bearings produced in a certain plant have a mean of 24.50 mm and a standard deviation of
0.15 mm. In what interval will the diameters of acceptable ball bearings fall if the manufacturer rejects the
smallest 2.5% and largest 0.15%? (Assume a normal distribution)
a. 24.05–24.80
c. 24.20–24.80
b. 24.05–24.95
d. 24.20–24.95
____ 13. A university accepts only applicants scoring in the top 16% on an entrance test. Each year the test scores are
normally distributed with a standard deviation of 30. What is the highest value that the mean can have for
Fred to be accepted with a score of 520?
a. 460
c. 520
b. 490
d. 550
2
____ 14. For X~N (5, 2 ) the z-score of x = 4.2 is
a. 0.4
c. 0.2
b. 0.2
d. 0.4
____ 15. The z-score corresponding to the 44th percentile is
a. 2.62
c. 0.44
b. 0.15
d. 4.40
____ 16. Given a normally-distributed data set whose mean is 40 and whose standard deviation is 8, what value of x
would have a z-score of 1.25?
a. 10
c. 30
b. 10
d. 50
____ 17. The heights of men, in centimetres, are normally distributed with a mean of 175 and a standard deviation of
20. If Mario is 180 cm tall, what percent of men is he taller than?
a. 0.62%
c. 59.87%
b. 40.13%
d. 99.38%
____ 18. The volume of cola in 355-mL cans is normally distributed with a standard deviation of 3 mL. What percent
of cans have a volume greater than 359 mL?
a. 9.18%
c. 64.1%
b. 35.9%
d. 90.82%
____ 19. To earn a scholarship, Luc needs to score in the top 8% on an entrance test. If test marks are normally
distributed with a mean of 500 and a standard deviation of 38, what mark (to the nearest whole number) is he
aiming for?
a. 446
c. 553
b. 447
d. 554
2
____ 20. If X~N(40, 3 ), what percent of the data are between 36 and 41?
a. 9.18%
c. 53.75%
b. 18.81%
d. 54.38%
____ 21. Find the percentile corresponding to x = 15 if X~N(12, 2.62).
a. 12th
c. 87th
b. 13th
d. 86th
____ 22. The number of candies in a bag is normally distributed with a mean of 200 and a standard deviation of 3. In
what percentile is a bag with 205 candies?
a. 2nd
c. 71st
b. 70th
d. 95th
____ 23. The masses of bolts made in a plant are normally distributed. Bolts will be rejected if their z-scores are greater
than 2.15 or less than 2.10. What percent of bolts will be rejected?
a. 0%
c. 1.79%
b. 1.58%
d. 3.37%
____ 24. The diameters of inflated balloons, in millimetres, are normally distributed with a mean of 200 and a standard
deviation of 12. Balloons will burst if their diameters exceed 210. What percent of balloons will burst?
a. 16.67%
c. 79.67%
b. 20.33%
d. 83.37%
____ 25. How many people in a group of 60 will have an IQ less than 92 if their IQs are normally distributed with a
mean of 100 and a standard deviation of 15?
a. 18
c. 30
b. 29
d. 42
____ 26. The diameters of the lead in 1500, 0.7-mm mechanical pencils are normally distributed with a standard
deviation of 0.02. How many of these pencils will have lead diameters greater than 0.75?
a. 2.5
c. 99
b. 9
d. 1491
____ 27. The heights, in centimetres, of the 700 female students in a high school are normally distributed with a mean
of 158 and a standard deviation of 6. Approximately how many of these students have a height between 151
cm and 165 cm?
a. 528
c. 536
b. 534
d. 530
Short Answer
28. If X~N(10, 22), what is the mean?
29. X~N(12.2,
) and 99.7% of data fall within the interval 11.6–12.8. What is the standard deviation?
2
30. If X~N(105, 4 ), then what percent of the data are contained in the interval 97–105?
31. For X~N
, what percent of the data fall between
and
?
32. The time that a certain top sprinter takes to run the 100-m dash is normally distributed with a mean of 9.8 s
and a standard deviation of 0.2 s. In what percent of his sprints will his time be less than 10.0 s?
33. Calculate the z-score, to one decimal place, of x = 7.2 if
= 8.1 and
= 3.
34. Ravi’s math contest result put him in the 97th percentile. If 4000 students competed, how many had a score
higher than Ravi’s score?
35. What percentile corresponds to a normal z-score of 1.24?
36. What normal z-score corresponds to the 14th percentile?
37. Suppose X~N(50, 42). What value of x would have a z-score of 2.10?
38. The numbers of peanuts in a bag are normally distributed with a mean of 150 and a standard deviation of 8.
What percent of bags have fewer than 140 peanuts?
39. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What IQ (to the nearest
whole number) is required to be in the top 15?
40. In X~N(12, 22), what percent of the data is between 10 and 13?
Sample Questions Mastery #4
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
C
A
C
A
B
C
B
A
D
C
A
D
B
A
B
C
C
A
D
C
C
D
D
B
A
B
D
SHORT ANSWER
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
The mean is 10.
The standard deviation is 0.2.
The percent of the data contained in the interval is 47.5%.
The percent of the data that fall between
and
is 81.5%.
Approximately 84% of his sprints will be less than 10.0 s.
The z-score is 0.3.
The number of students with a score higher than Ravi’s is 120.
The percentile that corresponds to a z-score of 1.24 is the 89th percentile.
The normal z-score is z = 1.08.
The value of x would be 58.4.
38. The percent of bags that have fewer than 140 peanuts is 10.56%.
39. An IQ of 116 is required to be in the top 15.
40. The percent of the data between 10 and 13 is 53.28%.