Question 1

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

Accepted Answer

The normal distribution is symmetric about its mean.

Question 2

Suppose a random variable $$X$$ follows a normal distribution with mean $$\mu = 50$$ and standard deviation $$\sigma = 10. $$What is the z-score for $$x = 70$$?

Accepted Answer

$$z = 2$$

Question 3

What does the area under the probability density function (pdf) of a continuous random variable represent?

Accepted Answer

The total probability, which must equal 1

Question 4

If $$X \sim N(100, 15)$$, what is the probability that $$X = 100$$?

Accepted Answer

0

Question 5

Which of the following best describes the Empirical Rule for a normal distribution?

Accepted Answer

All of the above are correct.

Question 6

A standardized test has scores that are normally distributed with mean $$\mu = 500$$ and standard deviation $$\sigma = 100. $$What is the probability that a randomly selected student scores less than 500?

Accepted Answer

0.5

Question 7

Which of the following is the correct formula for converting a value $$x to a z-$$score in a normal distribution?

Accepted Answer

$$z = (x - \mu) / \sigma$$

Question 8

In a normal distribution, which of the following statements is TRUE about the mean, median, and mode?

Accepted Answer

The mean, median, and mode are all equal.

Question 9

A hospital records the birth weights of newborns, which are normally distributed with mean $$\mu = 3.5 kg $$and standard deviation $$\sigma = 0.5 kg. $$What is the z-score for a baby weighing 4.0 kg?

Accepted Answer

$$z = 1$$

Question 10

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

Accepted Answer

It is always skewed to the left.

Question 11

If $$X is a $$continuous random variable, what is $$P(X = c)$$ for any constant $$c$$?

Accepted Answer

0

Question 12

A pharmaceutical company finds that the time it takes for a drug to take effect is normally distributed with mean $$\mu = 30$$ minutes and standard deviation $$\sigma = 5$$ minutes. What is the probability that the drug takes more than 40 minutes to take effect?

Accepted Answer

Approximately 0.0228

Question 13

Which of the following best describes the cumulative distribution function (cdf) for a continuous random variable?

Accepted Answer

It gives the probability that $$X is $$less than or equal to a specific value.

Question 14

A university wants to admit students whose test scores are in the top 2.5% of a normal distribution. Approximately what z-score should a student have to be admitted?

Accepted Answer

$$z \approx 1.96 or $$higher

Question 15

If the area to the left of $$x$$ under a normal curve is 0.80, what is the area to the right of $$x$$?

Accepted Answer

0.20

Question 16

Which of the following is a correct interpretation of $$P(X \u003c x)$$ for a continuous random variable $$X$$?

Accepted Answer

It is the area under the curve to the left of $$x.$$

Question 17

A machine produces metal rods with lengths that are normally distributed with mean $$\mu = 100 cm $$and standard deviation $$\sigma = 2 cm. $$What percentage of rods are expected to have lengths between 98 cm and 102 cm?

Accepted Answer

About 68%

Question 18

Which of the following phrases indicates the use of the inequality $$\geq$$?

Accepted Answer

"Is at least"

Question 19

If a value $$x$$ has a negative z-score in a normal distribution, what does this indicate?

Accepted Answer

The value is below the mean.

Question 20

A researcher is interested in the probability that a randomly selected adult has a cholesterol level between 180 mg/dL and 220 mg/dL. If cholesterol levels are normally distributed with mean $$\mu = 200 mg/dL $$and standard deviation $$\sigma = 20 mg/dL$$, which of the following expressions correctly represents the probability?

Accepted Answer

$$P(180 \u003c X \u003c 220)$$

Chapter 7: The Normal Distribution – Properties and Applications

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