Chapter 7

Which of the following are true because the normal probability distribution is symmetric about the mean? Select all that apply. Multiple select question. The shape to the left of the mean is a mirror image of the shape to the right of the mean. The area on each side of the mean equal one-half. The distribution approaches the x-axis, but never touches it. The total area under the curve is 1.00.

The shape to the left of the mean is a mirror image of the shape to the right of the mean. The area on each side of the mean equal one-half.

Multiple Choice Question The average weight of a Honeycrisp apple is 110 grams and the standard deviation is 20 grams. What is the z-value for an apple that weighs 140 grams? Multiple choice question. z = -1.5 z = 2.5 z = 30 z = 1.5

z = 1.5

The average score on an IQ test is 110 and the standard deviation is 10 grams. What is the z-value for a score of 130? Multiple choice question. z = 20 z = -2 z = 2 z = 3

z = 2

Which of the following formulas is used to convert a normally distributed random variable, X, to a z-value? Multiple choice question. z = X−σμ�-σμ X = z+μσ�+μσ z = X−μσ�-μσ z = √μ2+σ2

z = X−μ/σ

The formula for converting a normally distributed random variable X, to a z-value is z = X−μσ�-μσ. Match the variables to their description.

z a standard normal random variable X a normal random variable μ the mean of X σ the standard deviation of X 1 the standard deviation of z

A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 400 and 500? Multiple choice question. 0.2861 0.4625 0.2486 0.2139

0.2139 Reason:z=(400-560)/90=-1.78; z=(500-560)/90=-0.67. Use Excel function Normdist or z-tables (0.4625-0.2486)

A graduate school entrance exam has scores that are normally distributed with a mean of 560 and a standard deviation of 90. What percentage of examinees will score between 600 and 700? Multiple choice question. 0.4406 0.1700 0.2294 0.2706

0.2706

Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 490 and 560? Multiple choice question. 0.3400 0.7823 0.2177 0.2823

0.2823

Scores on a graduate school entrance exam follow a normal distribution with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen test taker will score between 560 and 640? Multiple choice question. 0.3133 0.8133 0.3400 0.1867

0.3133

Applicants for graduate school take a test that has scores which are normally distributed with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen applicant will score between 550 and 650? Multiple choice question. 68% 0.3851 0.6149 0.2975

0.3851 Reason:z=(550-560)/90=-0.11; z=(650-560)/90=1.00. Use Excel function Normdist or z-tables (0.3413+0.0438).

Applicants for graduate school take a test that has scores which are normally distributed with a mean of 560 and a standard deviation of 90. What is the probability that a randomly chosen applicant will score between 500 and 600? Multiple choice question. 95% 0.5814 0.4186 0.0786

0.4186

What percentage of the area under the normal curve is more than 1 standard deviation from the mean? Multiple choice question. Approximately 5% Approximately 68% Approximately 16% Approximately 32%

Approximately 32%

What percentage of the area under a normal curve is within 1, 2, and 3 standard deviations of the mean? Match the probabilities to the range for the Empirical Rule for the Normal distribution.

Approximately 68% matches Choice μ ± σ Approximately 95% matches Choice μ ± 2σ Approximately 99.7% matches Choice μ ± 3σ

Which of the following is true regarding continuous and discrete random variables. Multiple choice question. Continuous random variables can only take on a fixed number of values over a range. For continuous random variables probability is defined for individual values. Continuous and discrete random variables are usually found by counting. Continuous random variables usually result from measuring.

Continuous random variables usually result from measuring.

What do we mean when we say there is a "family" of normal distributions? Choose two of these statements. Multiple select question. The term "normal" refers to the fact that the area under the curve is one. Distributions may have different means and standard deviations but still be "normal" in shape. Any "bell" shaped curve is a Normal curve. A single equation describes all normal distributions.

Distributions may have different means and standard deviations but still be "normal" in shape. A single equation describes all normal distributions.

How would you describe the shape of the Normal Distribution? Multiple choice question. It is rectangular in shape, with limits at μ - σ and μ + σ. It is triangular in shape, with the peak at μ and a base width of 2σ. It is "bell" shaped, and symmetrical with the center at μ. It is "bell" shaped, with "tail" on the left side.

It is "bell" shaped, and symmetrical with the center at μ.

Where does the curve of the normal distribution touch the x-axis? Multiple choice question. It never touches, but approaches asymptotically in both directions. At μ + σ and μ - σ. At x equals zero and x equals 2σ. It depends on the height, because the area under the curve must be one.

It never touches, but approaches asymptotically in both directions.

What are the upper and lower limits of the random variable for the Normal distribution? Multiple choice question. The values x = a and x = b. No limits. It is asymptotic in both directions. The limits are μ plus or minus σ. Zero and one, because the area under the curve represents a probability.

No limits. It is asymptotic in both directions.

Since the normal probability distribution is symmetrical about the mean, which of the following are true? Select all that apply. Multiple choice question. The area under each side is determined by the standard deviation. The area on each side of the mean is 0.5. The total area under the curve is less than 1.00 since it never touches the x-axis. The shape of the distribution is only dependent upon the mean.

The area on each side of the mean is 0.5.

How does the Standard Normal distribution relate to any normal probability distribution? Choose all that apply, Multiple select question. The areas are equal to 1. The means are equal to 0 and the standard deviations are equal to 1. The range is μ ± σ. A normal probability distribution can be converted into a standard normal distribution.

The areas are equal to 1. A normal probability distribution can be converted into a standard normal distribution.

Which is the best definition of the z-value? Multiple choice question. Defined as the mean, μ plus or minus the standard deviation, σ. The number of times some event occurs during a specified interval The distance between a value x and the mean, μ, divided by the standard deviation, σ The z-value from the probability of success and the number of samples.

The distance between a value x and the mean, μ, divided by the standard deviation, σ

What determines the width and location of the Normal Distribution? Multiple choice question. The mean (μ) determines the location and the standard deviation (σ) determines the width. The standard deviation (σ) determine the location on the x axis, and the mean (μ) determines the width. The width is determined by the upper and lower bounds of x, and the location by the mean.

The mean (μ) determines the location and the standard deviation (σ) determines the width.

Which of the following statements are true of the Standard Normal Distribution? Multiple select question. The mean (μ) is zero. The standard deviation (σ) is 1 The mean is μ = 1. The range is μ ± σ.

The mean (μ) is zero. The standard deviation (σ) is 1

Which one of the following is a result of the the normal probability distribution being bell-shaped? Multiple choice question. The area on each side of the mean equals 1.00. The mean is further in the right tail than the median is. The mean, median, and mode are at the center. The area on the right side of the mean is greater than the area on the left.

The mean, median, and mode are at the center.

Which of the following are true because the normal probability distribution is symmetric about the mean? Select all that apply. Multiple select question. The total area under the curve is 1.00. The shape to the left of the mean is a mirror image of the shape to the right of the mean. The distribution approaches the x-axis, but never touches it. The area on each side of the mean equal one-half.

The shape to the left of the mean is a mirror image of the shape to the right of the mean. The area on each side of the mean equal one-half.

Which of the following is an example of a continuous random variable? Multiple choice question. The number of bedrooms in a house. The zip code of a house. The square footage of a house. Whether or not a house has a pool.

The square footage of a house.

What is the purpose of converting a random variable to a z-value? Select all that apply. Multiple select question. To convert a normal distribution to a uniform distribution To express the distance from the mean in terms of the standard deviation. To standardize the random variable so that the sum of the probabilities is one. To compare a normal distribution to a standard normal distribution.

To express the distance from the mean in terms of the standard deviation. To compare a normal distribution to a standard normal distribution.