Question 1

Which of the following statements best describes a continuous random variable?

Accepted Answer

It can take on any value within a given interval.

Question 2

For a normal distribution with mean $$\mu = 50$$ and standard deviation $$\sigma = 8$$, what is the $$z-$$score for $$x = 66$$?

Accepted Answer

$$z = \frac{66 - 50}{8} = 2$$

Question 3

Which of the following is NOT a characteristic of the normal probability distribution?

Accepted Answer

The total area under the curve is less than 1.

Question 4

A company finds that the time to complete a task is normally distributed with $$\mu = 30$$ minutes and $$\sigma = 5$$ minutes. What is the probability that a randomly selected task will take more than 37 minutes? (Use the standard normal table: $$P(z \leq 1.4) = 0.9192)$$

Accepted Answer

0.0808

Question 5

Which formula is used to convert a value $$x$$ from a normal distribution to a $$z-$$score?

Accepted Answer

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

Question 6

The empirical rule states that for a normal distribution, approximately what percentage of values fall within two standard deviations of the mean?

Accepted Answer

95%

Question 7

Suppose the annual snowfall in a city is normally distributed with $$\mu = 46$$ inches and $$\sigma = 18.5$$ inches. What is the $$z-$$score for a year with 70 inches of snow?

Accepted Answer

$$z = \frac{70 - 46}{18.5} = 1.30$$

Question 8

A random variable $$X is $$uniformly distributed between $$a = 10$$ and $$b = 20. $$What is the probability density function $$f(x)$$ for $$10 \leq x \leq 20$$?

Accepted Answer

$$f(x) = \frac{1}{20 - 10} = 0.1$$

Question 9

Which of the following scenarios is best modeled by an exponential distribution?

Accepted Answer

The time between arrivals of buses at a station.

Question 10

If $$X is a $$continuous random variable, what is the probability that $$X$$ takes on any single specific value?

Accepted Answer

0

Question 11

A business wants to use the normal distribution to approximate a binomial distribution. Which condition must be satisfied?

Accepted Answer

$$np \geq 5$$ and $$nq \geq 5$$

Question 12

A company’s quality control department finds that 6% of orders are incorrect. For a sample of 120 orders, what is the mean and standard deviation for the number of incorrect orders?

Accepted Answer

$$\mu = 7.2$$, $$\sigma = 2.60$$

Question 13

If the probability that $$z \leq 0.67 is 0.7486$$, what is the probability that $$z \u003e 0.67$$?

Accepted Answer

0.2514

Question 14

Which Excel function would you use to find the cumulative probability for $$x = 48$$, $$\mu = 45$$, $$\sigma = 5 in a $$normal distribution?

Accepted Answer

=NORM.DIST(48, 45, 5, TRUE)

Question 15

Suppose the mean income for a group of workers is $$45,000 with a standard deviation of 5$$,000. What is the probability that a randomly selected worker earns between $$38,000 and 48$$,000? (Use $$z_{38} = -1.40$$, $$z_{48} = 0.60$$, $$P(z \leq 0.60) = 0.7257$$, $$P(z \leq -1.40) = 0.0808)$$

Accepted Answer

0.6449

Question 16

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

Accepted Answer

The distribution becomes wider and flatter.

Question 17

A weight-loss program claims an average loss of 5.0 lb with a standard deviation of 3.0 lb after two weeks. What is the probability that a person will lose more than 7.0 lb? (Use $$z = \frac{7 - 5}{3} = 0.67$$, $$P(z \leq 0.67) = 0.7486)$$

Accepted Answer

0.2514

Question 18

If $$P(z \leq -0.70) = 0.2420$$, what is the probability that $$z \u003e -0.70$$?

Accepted Answer

0.7580

Question 19

Which of the following is a correct application of the continuity correction when using the normal distribution to approximate a binomial probability for $$P(x = 9)$$?

Accepted Answer

Use $$P(8.5 \leq x \leq 9.5)$$

Continuous Probability Distributions: The Normal Distribution and Its Applications

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