Q: Suppose men's heights are normally distributed with $$\mu = 69.5$$ inches and $$\sigma = 2.4$$ inches. What ceiling height allows 95% of men to stand without bumping their heads?

$$x = 69.5 + 1.645 \times 2.4 = 73.45$$ inches

Question 1

Which of the following statements best describes the standard normal distribution?

Accepted Answer

It is a normal distribution with mean $$\mu = 0$$ and standard deviation $$\sigma = 1.$$

Question 2

Given a normal distribution with mean $$\mu = 50$$ and standard deviation $$\sigma = 5$$, what is the z-score for $$x = 60$$?

Accepted Answer

$$z = \frac{60 - 50}{5} = 2$$

Question 3

Which formula is used to convert a value $$x$$ from a normal distribution with mean $$\mu$$ and standard deviation $$\sigma to a z-$$score?

Accepted Answer

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

Question 4

A bone density test yields a z-score of 1.27. What is the probability that a randomly selected adult has a bone density test score less than 1.27?

Accepted Answer

0.8980

Question 5

If the area to the left of $$z = 2.06$$ under the standard normal curve is desired, which of the following is correct?

Accepted Answer

Look up $$z = 2.06 in $$the standard normal table and use the area given.

Question 6

A voltage level is uniformly distributed between 123 and 125 volts. What is the probability that a randomly selected voltage is greater than 124.5 volts?

Accepted Answer

0.25

Question 7

Which of the following is NOT a property of a density curve?

Accepted Answer

The total area under the curve is less than 1.

Question 8

Suppose men's heights are normally distributed with $$\mu = 69.5$$ inches and $$\sigma = 2.4$$ inches. What ceiling height allows 95% of men to stand without bumping their heads?

Accepted Answer

$$x = 69.5 + 1.645 	imes 2.4 = 73.45$$ inches

Question 9

What is the mathematical equation for the normal distribution?

Accepted Answer

$$y = \frac{e$$^{-\frac{(x-\mu)^2}$${2\$$sigma^2$$}}}{\sigma \sqrt{2\pi}}$$

Question 10

If the area to the left of a z-score is 0.975, what is the corresponding z-score?

Accepted Answer

1.96

Question 11

A household generates between 27 and 31 pounds of newspaper per month. If the mean is 28 pounds and the standard deviation is 2 pounds, what is the probability that a randomly selected household falls in this range?

Accepted Answer

0.6247

Question 12

Which of the following best describes a uniform distribution?

Accepted Answer

A continuous random variable with values spread evenly over the range of possible values.

Question 13

What is the critical value $$z_{0.025}$$ for the standard normal distribution?

Accepted Answer

1.96

Question 14

If the area to the right of a z-score is 0.025, what is the cumulative area to the left?

Accepted Answer

0.975

Question 15

A 500-sq-ft apartment in Bloomington has a mean rent of $$620 and a standard deviation of 100. $$What is the probability that rent is more than $500?

Accepted Answer

0.9772

Question 16

Which of the following is true about the shapes of normal distributions with different means and standard deviations?

Accepted Answer

Distributions with larger standard deviations are wider and flatter.

Question 17

If $$P(z \u003c a) = 0.05$$, what is the value of $$a ($$rounded to two decimal places)?

Accepted Answer

-1.645

Question 18

Which of the following best describes the correspondence between area and probability in a continuous probability distribution?

Accepted Answer

The probability of an event is equal to the area under the density curve for that event.

Study Guide: The Normal Probability Distributions in Introductory Statistics

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