Q: Which formula correctly represents the area under a uniform distribution from $$a to$$ $$b$$?

$$\text{Area} = (b - a) \times \text{height}$$

Question 1

Which of the following is NOT a property of the standard normal distribution?

Accepted Answer

The mean is equal to 0.

Question 2

A continuous random variable has a uniform distribution between $$a = 2$$ and $$b = 8. $$What is the height of the density curve?

Accepted Answer

$$\frac{1}{6}$$

Question 3

If the area under a density curve between $$x = 3$$ and $$x = 7 is$$ $$0.5$$, what is the probability that a randomly selected value falls between $$x = 3$$ and $$x = 7$$?

Accepted Answer

0.5

Question 4

The waiting time for airport security is uniformly distributed between 0 and 5 minutes. What is the probability that a randomly selected passenger waits more than 3 minutes?

Accepted Answer

0.4

Question 5

Which formula correctly represents the area under a uniform distribution from $$a to$$ $$b$$?

Accepted Answer

$$	ext{Area} = (b - a) 	imes 	ext{height}$$

Question 6

A bone density test result is normally distributed with $$\mu = 0$$ and $$\sigma = 1. $$What is the probability that a randomly selected person has a z-score less than 1.27?

Accepted Answer

0.8980

Question 7

Given a standard normal distribution, what is the probability that $$z \u003e -1.00$$?

Accepted Answer

0.8413

Question 8

For a standard normal distribution, what is $$P(-2.50 \u003c z \u003c -1.00)$$?

Accepted Answer

0.1525

Question 9

Which of the following best describes the relationship between area under a density curve and probability?

Accepted Answer

Area under the curve equals the probability of the corresponding event.

Question 10

If you want to find the z-score corresponding to the 95th percentile in a standard normal distribution, which Excel function would you use?

Accepted Answer

NORM.INV

Question 11

What is the value of $$z_{0.025} in $$the standard normal distribution?

Accepted Answer

1.96

Question 12

Which notation represents the probability that a z-score is greater than $$a$$?

Accepted Answer

$$P(z \u003e a)$$

Question 13

A satellite crashes at a random point on Earth. If the area of land is 54,225,000 square miles and the area of water is 142,725,000 square miles, what is the probability it crashes on land?

Accepted Answer

0.275

Question 14

Which of the following is true about the graph of a uniform distribution?

Accepted Answer

It is rectangular.

Question 15

If the cumulative area to the left of $$z = -1.00 is$$ $$0.1587$$, what is the cumulative area to the right?

Accepted Answer

0.8413

Question 16

Which of the following steps is NOT necessary when finding a z-score from a known area using Table A-2?

Accepted Answer

Multiply the area by the mean.

Question 17

A bone density reading between $$z = -1.00$$ and $$z = -2.50$$ indicates osteopenia. What percentage of people have osteopenia?

Accepted Answer

15.25%

Question 18

If you want to find the critical value $$z_{0.1}$$, which cumulative area should you use in Table A-2?

Accepted Answer

0.9

Question 19

Which of the following best describes a density curve?

Accepted Answer

A graph of any continuous probability distribution with total area equal to 1.

Question 20

If the area to the left of $$z = 1.645 is$$ $$0.95$$, what does this mean in terms of percentiles?

Accepted Answer

1.645 is the 95th percentile.

6.1 Normal Probability Distributions: The Standard Normal Distribution and Applications

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