Question 1

Which of the following statements correctly describes the inflection points of a normal curve?

Accepted Answer

They occur at $$x = \mu - \sigma$$ and $$x = \mu + \sigma.$$

Question 2

Suppose the heights of three-year-old females are normally distributed with mean $$\mu = 38.72$$ inches and standard deviation $$\sigma = 3.17$$ inches. What is the $$z-$$score for a child who is 35 inches tall?

Accepted Answer

$$z = \dfrac{35 - 38.72}{3.17} \approx -1.17$$

Question 3

Which property is NOT true of the normal density curve?

Accepted Answer

It has two peaks at $$x = \mu \pm \sigma.$$

Question 4

According to the Empirical Rule, approximately what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 5

If the area under the normal curve to the right of $$x = 200 is$$ $$0.2903$$, what does this area represent in the context of cholesterol levels for males aged 20-29?

Accepted Answer

The proportion of males with cholesterol greater than 200 mg/dL.

Question 6

Given a normal random variable $$X$$ with mean $$\mu$$ and standard deviation $$\sigma$$, which formula correctly standardizes $$X to a$$ $$z-$$score?

Accepted Answer

$$z = \dfrac{X - \mu}{\sigma}$$

Question 7

A pediatrician wants to know the proportion of three-year-old females with heights between 35 and 40 inches. If the area under the normal curve between these values is $$0.5365$$, what is the correct interpretation?

Accepted Answer

About 54% of three-year-old females are between 35 and 40 inches tall.

Question 8

If SAT math scores are normally distributed with mean $$516$$ and standard deviation $$116$$, what SAT score corresponds to the 95th percentile?

Accepted Answer

$$707$$

Question 9

What is the value of $$z_{0.10}$$, the $$z-$$score such that the area to the right is $$0.10$$?

Accepted Answer

$$z_{0.10} = 1.28$$

Question 10

Which of the following is true about the probability of a continuous random variable taking a specific value?

Accepted Answer

$$P(X = a) = 0$$

Question 11

A normal curve is shifted three units to the right but maintains its shape. Which parameter was changed?

Accepted Answer

The mean $$\mu$$ was increased.

Question 12

Which formula represents the normal probability density function (pdf)?

Accepted Answer

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

Question 13

If the area under the standard normal curve to the left of $$z = 1.33 is$$ $$0.9082$$, what is the area to the right of $$z = 1.33$$?

Accepted Answer

$$0.0918$$

Question 14

A child whose height is 35 inches is at the 12th percentile. What does this mean?

Accepted Answer

12% of children are shorter than 35 inches.

Question 15

Which of the following best describes the effect of increasing the standard deviation $$\sigma of a $$normal distribution while keeping the mean $$\mu$$ constant?

Accepted Answer

The curve becomes flatter and more spread out.

Question 16

If the area under the normal curve between $$x = 35$$ and $$x = 40 is$$ $$0.5365$$, what is the probability that a randomly selected three-year-old female is between 35 and 40 inches tall?

Accepted Answer

$$0.5365$$

Question 17

Which statement about the area under the normal curve is correct?

Accepted Answer

The area under the curve to the left of the mean equals the area to the right of the mean, both are 0.5.

Chapter 7: The Normal Probability Distribution – Properties and Applications

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