Question 1

The total area of a normal probability distribution is

Accepted Answer

A)  between -3.0 and 3.0. 
B)  1.00. 
C)  dependent on a value of 'z'. 
D)  approximated by the binomial distribution.

Question 2

(i. The proportion of the area under a normal curve to the right of z = -1.21 is 0.8869. (ii) The proportion of the area under a normal curve to the left of z = 0.50 is 0.6941.
(iii) The proportion of the area under a normal curve to the left of z = -2.10 is 0.1179.

Accepted Answer

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)  (ii) and (iii) are correct statements but not (i).

Question 3

Normally distributed observations such as a person's weight, height or shoe size occur quite frequently in nature. Business people who are aware of this use it to their advantage. A purchasing agent for a college bookstore buying 300 golf shirts used the normal curve to decide on the order quantities for the various sizes. If men's average shirt size is 15.5 with a standard deviation of.50, how many shirts should be ordered in sizes over 16.5?

Accepted Answer

A)  7 
B)  8 
C)  9 
D)  10 
E)  6

Question 4

A sample of 500 evening students revealed that their annual incomes from employment in industry during the day were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. (i) 250 students earned more than $30,000.
(ii. 500 students earned between $20,000 and $40,000.
(iii) 11 students earned more than $36,000.

Accepted Answer

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)  (ii) and (iii) are correct statements but not (i).

Question 5

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

Accepted Answer

A)  1.0000 
B)  0.7408 
C)  0.1359 
D)  0.4772

Question 6

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. What is the income that separates the top 5% from the lower 95% of the incomes?

Accepted Answer

A)  $43,420 
B)  $47,320 
C)  $56,580 
D)  $52,680

Question 7

The mean of any uniform probability distribution is

Accepted Answer

A)  (b - a)/2 
B)  (a + b)/2 
C)   
D)  n$\pi$

Question 8

i. Asymptotic, means that the normal curve gets closer and closer to the X-axis but never actually touches it. ii. When referring to the normal probability function, there is not just one of them; there is a "family" of them.
iii. Some normal probability distributions have different arithmetic means and different standard deviations.

Accepted Answer

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)  (ii) and (iii) are correct statements but not (i). 
E)  (i), (ii), and (iii) are all false statements.

Question 9

Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Life test revealed that the mean mileage is 47,900 and the standard deviation of the normally distributed distribution of mileage is 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 5 percent of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce?

Accepted Answer

A)  44,528 
B)  32,960 
C)  49,621 
D)  40,922

Question 10

Determine the z-score associated with an area of 0.48 from the mean of a normal distribution to that positive z-score.

Accepted Answer

A)  2.05 
B)  2.06 
C)  0.1844 
D)  0.1808 
E)  2.60

Question 11

A major credit card company has determined that customers charge between $100 and $1,100 per month. Given that the average monthly amount charged is uniformly distributed, what percent of monthly charges are between $600 and $889?

Accepted Answer

A)  28.9% 
B)  20.8% 
C)  26.2% 
D)  29.3%

Question 12

Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years, (based on data from "Getting Things Fixed, "Consumer Reports). (i) The replacement time that separated the top 20% from the bottom 80% is 9.124 years.
(ii. The probability that a randomly selected TV will be replaced after more than 10.0 years is 0.0505.

Accepted Answer

A)  (i) and (ii) are correct statements. 
B)  (i) is a correct statement but not (ii). 
C)  (ii) is a correct statement but not (i). 
D)  (i) and (ii) are false statements.

Question 13

Tabulation of a strike vote showed that 90% of those voting cast their ballot in favour of strike action. You take a sample of 50 voters. Assume this to be a binomial distribution. What is the mean for this distribution?

Accepted Answer

A)  450 
B)  90 
C)  45 
D)  There is no mean for this type of distribution

Question 14

A cola-dispensing machine is set to dispense a mean of 2.02 litres into a container labelled 2 liters. Actual quantities dispensed vary and the amounts are normally distributed with a standard deviation of 0.015 litres. What is the probability a container will have less than 2 litres?

Accepted Answer

A)  0.0918 
B)  0.3413 
C)  0.1926 
D)  0.8741

Question 15

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?

Accepted Answer

A)  137 
B)  273 
C)  113 
D)  387

Question 16

A major credit card company has determined that customers charge between $100 and $1,100 per month. Given that the average monthly amount charged is uniformly distributed, what is the standard deviation of the monthly amount charged?

Accepted Answer

A)  298.67 
B)  275.57 
C)  267.88 
D)  288.67

Question 17

One classic use of the normal distribution is inspired by a letter to Dear Abbey in which a wife claimed to have given birth 308 days after a brief visit from her husband, who was serving in the Navy. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. Given this information. (i) the probability of a pregnancy lasting 300 days or longer is 0.0166.
(ii. The result suggests that the husband is not the father of the child.

Accepted Answer

A)  (i) and (ii) are correct statements. 
B)  (i) is a correct statement but not (ii). 
C)  (ii) is a correct statement but not (i). 
D)  (i) and (ii) are false statements.

Question 18

Normally distributed observations such as a person's weight, height, or shoe size occur quite frequently in nature. Business people who are aware of this use it to their advantage. A purchasing agent for a large retailer buying 15,000 pairs of women's shoes used the normal curve to decide on the order quantities for the various sizes. If women's average shoe size is 7.5 with a standard deviation of 1.5, how many pairs should be ordered between sizes 6.5 and 9?

Accepted Answer

A)  8640 
B)  8849 
C)  8664 
D)  8864 
E)  8940

Question 19

(i. The mean of a normal probability distribution is 60 and the standard deviation is 5. 95.44 percent of observations lie between 50 and 75. (ii) A z-value of -2.00 indicates that corresponding X value lies to the left of the mean.
(iii) One of the properties of the normal curve is that it gets closer to the horizontal axis, but never touches it. This property of the normal curve is called asymptotic.

Accepted Answer