Question 1

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

Accepted Answer

The mean, median, and mode are equal.

Question 2

A standard normal distribution has which of the following characteristics?

Accepted Answer

Mean = 0, Standard deviation = 1

Question 3

Given a normal distribution with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, what is the z-score for $$x = 130$$?

Accepted Answer

$$z = \frac{130 - 100}{15} = 2$$

Question 4

If the area to the left of $$z = 1.15$$ under the standard normal curve is $$0.8749$$, what is the area to the right of $$z = 1.15$$?

Accepted Answer

$$0.1251$$

Question 5

Which of the following best describes the Empirical Rule for a normal distribution?

Accepted Answer

All of the above.

Question 6

A continuous random variable is best described as:

Accepted Answer

A variable that can take on any value within an interval.

Question 7

Which of the following is a requirement for a probability density function (PDF)?

Accepted Answer

The total area under the curve must be equal to 1.

Question 8

If a normal distribution has a mean of 450 and a standard deviation of 27, what is the approximate range of values that contains about 95% of the data?

Accepted Answer

$$[396, 504]$$

Question 9

Which of the following statements about the normal curve is FALSE?

Accepted Answer

The curve is always skewed to the right.

Question 10

To find the area between two z-scores $$z_1$$ and $$z_2$$ $$(z_2$ \u003e z_1$)$$ under the standard normal curve, you should:

Accepted Answer

Subtract the area for $$z_1$$ from the area for $$z_2.$$

Question 11

A hospital records the time (in hours) patients spend in the emergency room. If this time is normally distributed with mean $$\mu = 3$$ and standard deviation $$\sigma = 0.5$$, what is the probability that a randomly selected patient spends less than 2 hours in the ER? (Use the z-score formula and standard normal table.)

Accepted Answer

First, calculate $$z = \frac{2 - 3}{0.5} = -2. $$The area to the left of $$z = -2 is $$approximately $$0.0228.$$

Question 12

Which of the following best describes an inflection point on the normal curve?

Accepted Answer

The point where the curve changes from curving upward to curving downward.

Question 13

A researcher wants to find the probability that a randomly selected value from a standard normal distribution is greater than $$z = 0.85. $$Which of the following steps is correct?

Accepted Answer

Find the area to the left of $$z = 0.85$$ and subtract it from 1.

Question 14

If the cumulative area for $$z = 0 is$$ $$0.5000$$, what does this represent?

Accepted Answer

Half of the data falls below the mean.

Question 15

A company finds that the weights of its packaged cereal are normally distributed with mean $$\mu = 500$$ grams and standard deviation $$\sigma = 10$$ grams. What is the probability that a randomly selected box weighs more than 520 grams?

Accepted Answer

Calculate $$z = \frac{520 - 500}{10} = 2. $$The area to the right of $$z = 2 is$$ $$1 - 0.9772 = 0.0228.$$

Normal Probability Distributions: Study Guide

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