Question 1

The image above shows a histogram of scores with a superimposed curve. 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 were to increase while keeping the mean $$\mu$$ constant, what would happen to the shape of the curve?

Accepted Answer

The curve would spread out and become flatter.

Question 5

Which equation represents the probability density function (PDF) for the normal distribution depicted 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 researcher claims that the data in the image is normally distributed. Which method could be used to support this claim, according to the study materials?

Accepted Answer

Check if the histogram is bell-shaped and symmetric.

Question 7

If 99.7% of the data falls within three standard deviations of the mean in a normal distribution, what is the interval for a mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$?

Accepted Answer

$$100 \pm 45$$

Question 8

Which of the following is a correct interpretation of the area under the normal curve between two values $$a$$ and $$b$$?

Accepted Answer

It represents the probability that a measurement falls between $$a$$ and $$b.$$

Question 9

Which of the following is NOT a recommended method for checking normality of data, as described in the study materials?

Accepted Answer

Calculating the range and comparing it to the mean.

Question 10

If a dataset is normally distributed, which of the following statements is true?

Accepted Answer

About 50% of the data lies to the left of the mean.

Normal Distribution and Sampling Distribution of Means

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