Question 1

Which of the following best describes the distribution shown in the first two images (yellow bell-shaped curve)?

Accepted Answer

A normal (bell-shaped) distribution

Question 2

According to the third image, which z-score range is considered 'not significant' for a normal distribution?

Accepted Answer

$$-2 \leq z \leq 2$$

Question 3

A student scores a z-score of 2.5 on a test. According to the third image, how would this score be classified?

Accepted Answer

Significantly high value

Question 4

If a data value has a z-score of -2.8, what does this indicate about the value?

Accepted Answer

It is a significantly low value

Question 5

Which rule applies only to data that is approximately bell-shaped, as shown in the first image?

Accepted Answer

Empirical Rule

Question 6

For a normal distribution, what percentage of data falls within one standard deviation of the mean?

Accepted Answer

$$68\%$$

Question 7

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

Accepted Answer

$$z = 2$$

Question 8

If a value is more than 3 standard deviations from the mean in a normal distribution, how is it typically classified?

Accepted Answer

A possible outlier

Question 9

Which formula would you use to calculate the z-score for a sample data value $$x$$ with sample mean $$\bar{x}$$ and sample standard deviation $$s$$?

Accepted Answer

$$z = \frac{x - \bar{x}}{s}$$

Question 10

A data set has a mean of 50 and a standard deviation of 5. What is the z-score for a value of 40?

Accepted Answer

$$z = -2$$

Question 11

Which of the following statements is TRUE about the Empirical Rule?

Accepted Answer

It applies only to bell-shaped (normal) distributions.

Question 12

If a data set is not bell-shaped, which rule should you use to estimate the minimum proportion of data within $$k$$ standard deviations of the mean?

Accepted Answer

Chebyshev's Theorem

Question 13

Using Chebyshev's Theorem, what is the minimum proportion of data within 2 standard deviations of the mean for any distribution?

Accepted Answer

$$75\%$$

Question 14

A sample of exam scores has a mean of 80 and a standard deviation of 8. If a student scored 96, what is their z-score?

Accepted Answer

$$z = 2$$

Question 15

Which of the following is NOT a measure of variation?

Accepted Answer

Mean

Measures of Variation and Relative Standing in Statistics

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