Question 1

i. For a normal probability distribution, about 95 percent of the area under normal curve is within
Plus and minus two standard deviations of the mean and practically all (99.73 percent) of the area
Under the normal curve is within three standard deviations of the mean.
ii. The total area under the normal curve is 1.
iii. The mean of a normal probability distribution is 500 and the standard deviation is 10. About 68
Percent of the observations lie between 480 and 520.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Accepted Answer

(i) and (ii) are correct statements but (iii).

Question 2

An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life
For a particular use before they failed is 19.0 hours. The distribution of the lives approximated a
Normal distribution. The standard deviation of the distribution was 1.2 hours. About 95.44 percent of
The batteries failed between what two values?
A) 8.9 and 18.9
B) 12.2 and 14.2
C) 14.1 and 22.1
D) 16.6 and 21.4

Accepted Answer

16.6 and 21.4

Question 3

What is the area under the normal curve between z = 0.0 and z = 1.79?
A) 0.4633
B) 0.0367
C) 0.9599
D) 0.0401

Accepted Answer

0.4633

Question 4

A sample of 500 evening students revealed that their annual incomes were normally distributed
With a mean income of $50,000 and a standard deviation of $4,000. How many students earned
Between $47,000 and $53,000?
A) 137
B) 273
C) 113
D) 387

Accepted Answer

273

Question 5

The mean of a normal distribution is 400 kg. The standard deviation is 10 kg. What is the area
Between 415 kg and the mean of 400 kg?
A) 0.5000
B) 0.1932
C) 0.4332
D) 0.3413

Accepted Answer

0.4332

Question 6

What is the area under the normal curve between z = 0.0 and z = 2.0?
A) 1.0000
B) 0.7408
C) 0.1359
D) 0.4772

Accepted Answer

0.4772

Question 7

The distribution of the annual incomes of a group of middle management employees approximated
A normal distribution with a mean of $37,200 and a standard deviation of $800. About 68 percent of
The incomes lie between what two incomes?
A) $30,000 and $40,000
B) $36,400 and $38,000
C) $34,800 and $39,600
D) $35,600 and $38,800

Accepted Answer

$36,400 and $38,000

Question 8

What is the area under the normal curve between z = -1.0 and z = -2.0?
A) 0.0228
B) 0.3413
C) 0.1359
D) 0.4772

Accepted Answer

0.1359

Question 9

A national manufacturer of unattached garages discovered that the distribution of the lengths of
Time it takes two construction workers to erect the Red Barn model is approximately normally
Distributed with a mean of 32 hours and a standard deviation of 2 hours. What percent of the
Garages take between 32 and 34 hours to erect?
A) 16.29%
B) 76.71%
C) 3.14%
D) 34.13%

Accepted Answer

34.13%

Question 10

A sample of 500 evening students revealed that their annual incomes were normally distributed
With a mean income of $50,000 and a standard deviation of $4,000. How many students earned
Between $45,000 and $53,000?
A) 170
B) 273
C) 334
D) 387

Accepted Answer

334

Question 11

A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of
50 hours. If the service life of these light bulbs approximates a normal distribution, about what
Percent of the distribution will be between 600 hours and 900 hours?
A) 95%
B) 68%
C) 34%
D) 99.7%

Accepted Answer

99.7%

Question 12

The annual commissions per salesperson employed by a manufacturer of light machinery averaged
$40,000 with a standard deviation of $5,000. What percent of the sales persons earn between
$32,000 and $42,000?
A) 60.06%
B) 39.94%
C) 34.13%
D) 81.66%

Accepted Answer

60.06%

Question 13

The mean amount of gasoline and services charged by Key Reﬁning Company credit customers is
$70 per month. The distribution of amounts spent is approximately normal with a standard deviation
Of $10. What is the probability of selecting a credit card customer at random and ﬁnding the
Customer charged between $70 and $83?
A) 0.1962
B) 0.4032
C) 0.3413
D) 0.4750

Accepted Answer

0.4032

Question 14

What is the proportion of the total area under the normal curve within plus and minus two standard
Deviations of the mean?
A) 68%
B) 99.7%
C) 34%
D) 95%

Accepted Answer

95%

Question 15

The mean of a normal probability distribution is 500 and the standard deviation is 10. About 95
Percent of the observations lie between what two values?
A) 475 and 525
B) 480 and 520
C) 400 and 600
D) 350 and 650

Accepted Answer

480 and 520

Question 16

i. Disaster Airlines determined that the mean number of passengers per ﬂight is 152 with a standard
Deviation of ten passengers. Practically all ﬂights have between 142 and 162 passengers.
ii. The total area under the normal curve is less than 1.
iii. The mean of a normal probability distribution is 500 and the standard deviation is 10.
About 68 percent of the observations lie between 480 and 520.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Accepted Answer

(i), (ii), and (iii) are all false statements.

Question 17

The employees of Cartwright Manufacturing are awarded eﬃciency ratings. The distribution of the
Ratings approximates a normal distribution. The mean is 400, the standard deviation 50. What is the
Area under the normal curve between 400 and 482?
A) 0.5000
B) 0.4495
C) 0.3413
D) 0.4750

Accepted Answer

0.4495

Question 18

i. For a normal probability distribution, about 95 percent of the area under normal curve is within
Plus and minus two standard deviations of the mean and practically all (99.73 percent) of the area
Under the normal curve is within three standard deviations of the mean.
ii. The total area under the normal curve is 100%.
iii. The mean of a normal probability distribution is 500 and the standard deviation is 10.
About 95 percent of the observations lie between 480 and 520.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (i), (ii), and (iii) are all false statements.

Accepted Answer

(i) and (iii) are correct statements but (ii).

Question 19

For the normal distribution, the mean plus and minus 1.96 standard deviations will include about
What percent of the observations?
A) 50%
B) 99.7%
C) 95%
D) 68%

Accepted Answer

95%

Question 20

The seasonal output of a new experimental strain of pepper plants was carefully weighed. The
Mean weight per plant is 15.0 pounds, and the standard deviation of the normally distributed
Weights is 1.75 pounds. Of the 200 plants in the experiment, how many produced peppers weighing
Between 13 and 16 pounds?
A) 100
B) 118
C) 197
D) 53

Accepted Answer

118

Quiz 6: Discrete Probability Distributions

What is the area under the normal curve between z = 0.0 and z = 1.79?

A sample of 500 evening students revealed that their annual incomes were normally distributed With a mean income of $50,000 and a standard deviation of $4,000. How many students earned Between $47,000 and $53,000?

The mean of a normal distribution is 400 kg. The standard deviation is 10 kg. What is the area Between 415 kg and the mean of 400 kg?

What is the area under the normal curve between z = 0.0 and z = 2.0?

The distribution of the annual incomes of a group of middle management employees approximated A normal distribution with a mean of $37,200 and a standard deviation of $800. About 68 percent of The incomes lie between what two incomes?

What is the area under the normal curve between z = -1.0 and z = -2.0?

A sample of 500 evening students revealed that their annual incomes were normally distributed With a mean income of $50,000 and a standard deviation of $4,000. How many students earned Between $45,000 and $53,000?

A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. If the service life of these light bulbs approximates a normal distribution, about what Percent of the distribution will be between 600 hours and 900 hours?

The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000. What percent of the sales persons earn between $32,000 and $42,000?

What is the proportion of the total area under the normal curve within plus and minus two standard Deviations of the mean?

The mean of a normal probability distribution is 500 and the standard deviation is 10. About 95 Percent of the observations lie between what two values?

The employees of Cartwright Manufacturing are awarded eﬃciency ratings. The distribution of the Ratings approximates a normal distribution. The mean is 400, the standard deviation 50. What is the Area under the normal curve between 400 and 482?

For the normal distribution, the mean plus and minus 1.96 standard deviations will include about What percent of the observations?