Question 1

Which of the following best describes a discrete random variable?

Accepted Answer

A variable whose possible values are countable and finite or countably infinite.

Question 2

Which condition must be satisfied for a probability distribution of a discrete random variable $$X$$?

Accepted Answer

Each probability $$P(x)$$ must be between 0 and 1, and $$\sum P(x) = 1.$$

Question 3

For a continuous random variable $$X$$, what does the probability $$P(a \u003c X \u003c b)$$ represent?

Accepted Answer

The area under the curve $$y = f(x)$$ between $$x = a$$ and $$x = b.$$

Question 4

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

Accepted Answer

The curve touches the x-axis at $$\mu \pm 3\sigma.$$

Question 5

Given a normal distribution with mean $$\mu = 25$$ and standard deviation $$\sigma = 1.6$$, what percentage of values lie between $$\mu - \sigma$$ and $$\mu + \sigma$$?

Accepted Answer

68.26%

Question 6

What is the formula for converting an $$x$$ value from a normal distribution to a $$z-$$score?

Accepted Answer

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

Question 7

A survey finds that computer owners use their computers an average of 2.4 years before upgrading, with a standard deviation of 0.5 years. What is the probability that a randomly selected owner will upgrade in fewer than 2 years? (Assume normal distribution)

Accepted Answer

0.2119

Question 8

If the mean height of magnolia bushes is $$\mu = 8$$ feet and the standard deviation is $$\sigma = 0.7$$ feet, what is the interval that contains approximately 68% of the heights?

Accepted Answer

$$7.3 to$$ $$8.7$$ feet

Question 9

What is the cumulative area to the left of $$z = 2.71 in $$the standard normal distribution?

Accepted Answer

0.9966

Question 10

In the context of the normal distribution, what is the significance of the inflection points?

Accepted Answer

They mark where the curve changes from concave up to concave down.

Question 11

A civil service exam has scores normally distributed with $$\mu = 75$$ and $$\sigma = 6.5. $$What is the lowest score to be in the top 5%?

Accepted Answer

$$85.69$$

Question 12

Which equation represents the probability density function for the normal distribution?

Accepted Answer

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

Question 13

For a standard normal distribution, what is the area to the left of $$z = 0$$?

Accepted Answer

0.5000

Question 14

If a random variable $$X is $$uniformly distributed between 3 and 6, what is the probability that $$X$$ falls between 4 and 5?

Accepted Answer

$$\frac{1}{3}$$

Question 15

A shopper spends an average of 45 minutes in a store with a standard deviation of 12 minutes. What is the probability that a shopper spends between 24 and 54 minutes in the store?

Accepted Answer

0.7333

Question 16

What is the $$z-$$score corresponding to the 75th percentile?

Accepted Answer

0.675

Question 17

If the area under the normal curve between $$\mu - 2\sigma$$ and $$\mu + 2\sigma is $$approximately 95.46%, what is the probability that a randomly selected value falls outside this interval?

Accepted Answer

4.54%

Question 18

Which of the following statements about continuous random variables is TRUE?

Accepted Answer

The probability that a continuous random variable equals a specific value is zero.

Question 19

If a normal distribution has $$\mu = 67$$ mph and $$\sigma = 4$$ mph, what speed corresponds to a $$z-$$score of $$-2.33$$?

Accepted Answer

57.68 mph

Discrete and Continuous Random Variables, Probability Distributions, and the Normal Distribution

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