Question 1

The image above shows a histogram of scores with a smooth curve overlay. Based on the study materials, which of the following statements best describes the distribution shown in the image?

Accepted Answer

The distribution is approximately normal, as indicated by the bell-shaped and symmetric curve.

Question 2

Which of the following is NOT a property of the normal distribution as illustrated by the image?

Accepted Answer

The area under the curve is less than 1.

Question 3

Suppose the mean score in the distribution shown is $$\mu = 50$$ and the standard deviation is $$\sigma = 10. $$According to the empirical rule, approximately what percentage of scores fall between 40 and 60?

Accepted Answer

About 68%

Question 4

If the standard deviation $$\sigma of $$the distribution in the image increases while the mean $$\mu$$ stays the same, what happens to the shape of the curve?

Accepted Answer

The curve spreads out and becomes flatter.

Question 5

Which equation represents the probability density function (PDF) for the normal distribution shown in the image?

Accepted Answer

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

Question 6

A student claims that the histogram in the image is not normal because it has several outliers. Based on the study materials, how many outliers should a normal distribution typically have?

Accepted Answer

No more than one outlier.

Question 7

If you were to create a quantile-quantile (QQ) plot for the data in the histogram, what would you expect to see if the data is normally distributed?

Accepted Answer

The points would lie close to a straight line.

Question 8

Given a normal distribution $$N(100, 15^2$)$$, what is the probability that a randomly selected value falls within one standard deviation of the mean?

Accepted Answer

About 68%

Question 9

Which of the following methods is NOT used to check if data is approximately normal, according to the study materials?

Accepted Answer

Calculating the median absolute deviation

Question 10

If the mean of a normal distribution is increased while keeping the standard deviation constant, what happens to the curve?

Accepted Answer

The curve shifts to the right.

Question 11

A researcher collects test scores from a large class and plots a histogram similar to the one in the image. The histogram is bell-shaped and symmetric. What can the researcher conclude about the distribution of test scores?

Accepted Answer

The test scores are approximately normally distributed.

Question 12

Which of the following best describes the relationship between the mean, median, and mode in a normal distribution?

Accepted Answer

Mean = Median = Mode

Normal Distribution and Sampling Distribution of Means: Study Notes

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