ST370 quiz 3

Given that X ~ N(10, 2), P(X > 20) Select one: a. it is very unlikely to occur b. can happen 1/5 of the time c. cannot happen d. we cannot determine its probability

a.

Birthweights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birthweights between 125 oz and 140 oz is Select one: a. 0.136 b. 0.636 c. 0.477 d. 0.819

a. 0.136

A locomotive's "adhesion" is the locomotive's pulling force as a multiple of its weight. This is an important performance measure of a locomotive. A diesel locomotive model has adhesion which varies in actual use according to a Normal distribution with mean 0.37 and standard deviation 0.04. The first quartile for the adhesion distribution is Select one: a. 0.34 b. 0.25 c. 0.04 d. 0.29

a. 0.34

The scores on the Wechsler Adult Intelligence Scale are approximately Normal with μ = 100 and σ = 15. The proportion of adults with scores between 90 and 110 is closest to Select one: a. 0.5 b. 0.667 c. 0.432 d. 0.25

a. 0.5

The scores on the Wechsler Adult Intelligence Scale are approximately Normal with μ = 100 and σ = 15. How high a score is needed to be in the highest 5%? Select one: a. 124 b. 130 c. 115 d. 135

a. 124

The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. Using the 68−95−99.7 rule, if students are given 90 minutes to complete the exam, what percent of students will not finish? a. 2.5 % b. 5 % c. 32 % d. 0.0015 %

a. 2.5

Given that X ~ N(300, 15), find the 70th percentile. Select one: a. 307.87 b. 210.00 c. 324.96 d. 0.5244

a. 307.87

Using the standard normal distribution tables, the area under the standard Normal curve corresponding to -0.5 < Z < 1.2 is Select one: a. 0.2815 b. 0.5764 c. 0.3085 d. 0.8849

b. 0.5764

Given X ~ N (300, 15), find P(280 < X < 340). Select one: a. 0.2000 b. 0.9050 c. 0.7460 d. 0.9999

b. 0.9050

A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in such a box has a Normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight. How heavy does a box have to be for it to be labeled overweight? Select one: a. 34.40 oz b. 34.15 oz c. 31.85 oz d. 31.60 oz

b. 34.15

Given X ~ N(300, 15). The area to the right of x = 330 Select one: a. is the same as the area to the left of x = 270. b. is the same as the area to the left of x = 330. c. P(X > 330) is the same as the area to the right of z = 2 and to the left of X = 270. d. is the same as the area to the right of z = 2.

c.

Given X ~ N(300, 15). The area to the right of x = 330 Select one: a. is the same as the area to the left of x = 330. b. is the same as the area to the right of z = 2. c. P(X > 330) is the same as the area to the right of z = 2 and to the left of X = 270. d. is the same as the area to the left of x = 270.

c.

Given X ~ N(300, 15). What can be said of the median? Select one: a. It is less than the average b. It is the same as the mode. c. The mode = median and the mode = the mean. d. It is the same as the average

c.

Birthweights at a local hospital have a Normal distribution with a mean of 110 oz and a standard deviation of 15 oz. The proportion of infants with birthweights above 125 oz is Select one: a. 0.341 b. 0.5 c. 0.159 d. 0.841

c. 0.159

Scores on a university exam are Normally distributed with a mean of 68 and a standard deviation of 9. Using the 68-95-99.7 rule, what percentage of students score above 77? a. 32 b. 5 c. 16 d. 2.5

c. 16

A locomotive's "adhesion" is the locomotive's pulling force as a multiple of its weight. This is an important performance measure of a locomotive. A diesel locomotive model has adhesion which varies in actual use according to a Normal distribution with mean 0.37 and standard deviation 0.04. The percent of adhesions measured in use that is higher than 0.40 is closest to Select one: a. 75 % b. 37 % c. 23 % d. 77 %

c. 23%

A Normal density curve has which of the following properties? a. It has a peak centered on its mean. b. It is symmetric. c. The spread of the curve is proportional to the standard deviation. d. All of the above.

d all of the above

Given that X ~ N(300, 15), find the z-score associated with x = 290. Select one: a. -10 b. 10/15 c. 15/10 d. -10/15

d.

The scores on the Wechsler Adult Intelligence Scale are approximately Normal with μ = 100 and σ = 15. The proportion of adults with scores above 130 is closest to Select one: a. 0.95 b. 0.001 c. 0.05 d. 0.025

d. 0.025

A company produces packets of soap powder labeled "Giant Size 32 Ounces." The actual weight of soap powder in such a box has a Normal distribution with a mean of 33 oz and a standard deviation of 0.7 oz. To avoid having dissatisfied customers, the company says a box of soap is considered underweight if it weighs less than 32 oz. To avoid losing money, it labels the top 5% (the heaviest 5%) overweight. What proportion of boxes is underweight (i.e., weigh less than 32 oz)? Select one: a. 0.9236 b. 0.2420 c. 0.7580 d. 0.0764

d. 0.0764

Using the standard Normal distribution tables, what is the area under the standard Normal curve corresponding to Z < 0.75? Select one: a. 0.9599 b. 0.7734 c. 0.7500 d. 0.0401

d. 0.7734

Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to Z > -1.62 is a. 0.0044 b. 0.9956 c. 0.0526 d. 0.9474

d. 0.9474