Question 1

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

Accepted Answer

It has a mean of 1.

Question 2

Given a continuous random variable $$X$$ with probability density function $$f(x)$$, what is the probability that $$X$$ takes any exact value $$x_0$$?

Accepted Answer

$$P(X = x_0$) = 0$$

Question 3

Suppose waiting times at an airport security checkpoint are uniformly distributed 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

For a uniform distribution $$X \sim U(a, b)$$, what is the formula for the mean $$\mu$$?

Accepted Answer

$$\mu = \frac{a+b}{2}$$

Question 5

The probability density function (pdf) for a normal distribution $$X \sim N(\mu, \sigma) is$$:

Accepted Answer

$$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e$$^{-\frac{1}$${2} \left( \frac{x-\mu}{\sigma} \$$right)^2$$}$$

Question 6

A bone density test result is normally distributed with mean 0 and standard deviation 1. What is the probability that a randomly selected person has a test score less than 1.27?

Accepted Answer

$$0.8980$$

Question 7

For the standard normal distribution, what is the area to the right of $$z = -1.00$$?

Accepted Answer

$$0.8413$$

Question 8

If $$X is $$normally distributed with mean $$68.6$$ and standard deviation $$2.8$$, what is the $$z-$$score for $$X = 72$$?

Accepted Answer

$$z = 1.21$$

Question 9

Using the empirical rule, approximately what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

$$95.45\%$$

Question 10

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 $$z is $$between $$-2.50$$ and $$-1.00$$?

Accepted Answer

$$0.1525$$

Question 11

Which of the following best describes a cumulative probability?

Accepted Answer

$$Pr(X \u003c x)$$

Question 12

If the distribution of head circumference among male soldiers is normal with mean $$22.8$$ inches and standard deviation $$1.1$$ inches, what interval contains the middle $$98\% of $$head circumferences?

Accepted Answer

$$(20.24, 25.36)$$

Question 13

Given $$X \sim N(66.2, 3.8)$$, what is the height $$x$$ such that $$95\% of $$adults are shorter than $$x$$?

Accepted Answer

$$x = 72.5$$

Question 14

Which formula is used to convert a value $$x$$ from a normal distribution $$N(\mu, \sigma) to a $$standard normal $$z-$$score?

Accepted Answer

$$z = \frac{x-\mu}{\sigma}$$

Question 15

If $$X \sim N(530, 80)$$, what percent of $$X$$ values are between $$370$$ and $$690$$?

Accepted Answer

$$95\%$$

Question 16

If $$X \sim N(530, 80)$$, what percent of $$X$$ values are more than $$690$$?

Accepted Answer

$$2.5\%$$

Question 17

If the area to the left of $$z is$$ $$0.9500$$, what is the corresponding $$z-$$score (rounded to two decimal places)?

Accepted Answer

$$z = 1.65$$

Question 18

Which of the following statements about the normal distribution is FALSE?

Accepted Answer

The probability of any single exact value is greater than zero.

Normal Probability Distributions: Concepts, Properties, and Applications

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