Question 1

Which of the following statements best describes a normal distribution?

Accepted Answer

It is a symmetric, bell-shaped curve that is completely determined by its mean and standard deviation.

Question 2

Given a normal distribution with mean $$\mu = 52$$ and standard deviation $$\sigma = 6$$, what is the value on the x-axis that is two standard deviations above the mean?

Accepted Answer

$$64$$

Question 3

What happens to the shape of a normal curve as the standard deviation increases, while the mean remains the same?

Accepted Answer

The curve becomes shorter and wider.

Question 4

Which of the following is NOT a property of the standard normal curve?

Accepted Answer

The total area under the curve is $$2.0000.$$

Question 5

If a variable $$x is $$normally distributed with mean $$\mu$$ and standard deviation $$\sigma$$, what is the formula for converting $$x to a$$ $$z-$$score?

Accepted Answer

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

Question 6

Suppose the heights of adult women are normally distributed with $$\mu = 64$$ inches and $$\sigma = 3$$ inches. What is the $$z-$$score for a woman who is $$70$$ inches tall?

Accepted Answer

$$z = 2$$

Question 7

Why does a histogram of a continuous variable appear more like a smooth curve as the number of groups (bins) increases?

Accepted Answer

Because the rectangles become narrower and their tops get closer together, approximating a curve.

Question 8

A normal distribution has $$\mu = 100$$ and $$\sigma = 15. $$What is the value at $$\mu - 3\sigma$$?

Accepted Answer

$$55$$

Question 9

Which of the following best explains why the normal distribution is so commonly observed in real-world data?

Accepted Answer

Many natural phenomena are influenced by many small, independent effects, which tend to produce a normal distribution.

Question 10

If you transform all $$x-$$values of a normal distribution to $$z-$$scores, what will be the mean and standard deviation of the resulting distribution?

Accepted Answer

Mean $$= 0$$, Standard deviation $$= 1$$

Question 11

A researcher claims that the area under the standard normal curve between $$z = -1$$ and $$z = 1 is $$approximately $$68\%. Is $$this claim correct?

Accepted Answer

Yes, because about $$68\% of $$the data in a normal distribution falls within one standard deviation of the mean.

Question 12

Which of the following would NOT change the shape of a normal curve?

Accepted Answer

Changing the mean while keeping the standard deviation the same.

Question 13

If a normal curve is described as 'tall and skinny,' what can you infer about its standard deviation?

Accepted Answer

The standard deviation is small.

Question 14

Which of the following is true about the mean, median, and mode of a normal distribution?

Accepted Answer

They are all equal.

Question 15

A continuous variable is measured more precisely (with more decimal places). What effect does this have on the histogram of the data?

Accepted Answer

The histogram appears more like a smooth curve.

The Normal Distribution and the Standard Normal Curve

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