Question 1

Which of the following is a property of the standard normal distribution?

Accepted Answer

It has a standard deviation equal to 1.

Question 2

For a continuous probability distribution, what does the area under the density curve between two points represent?

Accepted Answer

The probability that the random variable falls between those two points.

Question 3

Given a uniform distribution for waiting times at an airport security checkpoint between 0 and 5 minutes, what is the probability that a randomly selected passenger waits at least 2 minutes?

Accepted Answer

$$0.6$$

Question 4

Which formula correctly expresses the probability that a continuous random variable $$X$$ falls between $$a$$ and $$b$$?

Accepted Answer

$$P(a \u003c X \u003c b) = \int_{a}^{b} f(x) dx$$

Question 5

In a standard normal distribution, what is the probability that a randomly selected value is exactly equal to the mean?

Accepted Answer

$$0$$

Question 6

A bone density test result is measured as a $$z$$ score. If the cumulative area to the left of $$z = 1.27 is$$ $$0.8980$$, what percentage of people have bone density scores below $$1.27$$?

Accepted Answer

$$89.80\%$$

Question 7

For a uniform distribution between $$a$$ and $$b$$, what is the formula for the height of the density curve?

Accepted Answer

$$\frac{1}{b-a}$$

Question 8

If the area to the left of $$z = -1.00 is$$ $$0.1587$$, what is the probability that a randomly selected person has a bone density reading above $$z = -1.00$$?

Accepted Answer

$$0.8413$$

Question 9

Which of the following statements about the height of a density curve is true?

Accepted Answer

It does not represent probability; the area under the curve does.

Question 10

A continuous random variable $$X$$ has a uniform distribution on $$[0, 5]. $$What is the probability that $$X is $$between $$1$$ and $$4$$?

Accepted Answer

$$0.6$$

Question 11

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

Accepted Answer

It is skewed to the left.

Question 12

If the area to the left of $$z = -2.50 is$$ $$0.0062$$ and the area to the left of $$z = -1.00 is$$ $$0.1587$$, what is the probability that a randomly selected person has a bone density reading between $$z = -2.50$$ and $$z = -1.00$$?

Accepted Answer

$$0.1525$$

Question 13

What is the general rule for finding the area between two $$z$$ scores in a standard normal distribution?

Accepted Answer

Subtract the cumulative area to the left of the lower $$z$$ score from the cumulative area to the left of the higher $$z$$ score.

Question 14

Which of the following best describes a uniform distribution?

Accepted Answer

All values are equally likely within the range.

Question 15

If $$f(x) is a $$probability density function, which of the following must be true?

Accepted Answer

$$\int_{-\infty}^{\infty} f(x) dx = 1$$

Question 16

A critical value $$z_{\alpha} in $$the standard normal distribution is defined as:

Accepted Answer

The $$z$$ score with an area of $$\alpha to $$its right.

Normal Probability Distributions: Density Curves, Uniform and Standard Normal Distributions

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