Question 1

Why do we divide by $$N-1$$ instead of $$N$$ when calculating sample variance?

Accepted Answer

To compensate for the fact that sample means are usually closer to the sample values than the population mean, which would otherwise underestimate the variance.

Question 2

Which of the following is the correct formula for the standard deviation of a sample?

Accepted Answer

$$s = \sqrt{\frac{\sum (x_i - \overline{x})^2$}{N-1}}$$

Question 3

For a normal distribution, approximately what percentage of values fall within 2 standard deviations of the mean?

Accepted Answer

About 95%

Question 4

What is the main advantage of using z-scores?

Accepted Answer

They allow comparison across different distributions by expressing values in terms of standard deviations from the mean.

Question 5

Given a test with a mean of 60 and a standard deviation of 5, what is the z-score for a student who scored 70?

Accepted Answer

$$z = \frac{70 - 60}{5} = 2$$

Question 6

Which statement best describes the Central Limit Theorem?

Accepted Answer

The sampling distribution of the mean will be approximately normal for large sample sizes, regardless of the original distribution.

Question 7

If the probability of a traffic light being red, yellow, or green is 0.33 each, what is the probability of encountering a red light AND a green light in two consecutive passes?

Accepted Answer

$$0.33 	imes 0.33 = 0.1089$$

Question 8

Which of the following is a property of the normal distribution?

Accepted Answer

It is unimodal and symmetrical.

Question 9

What is the probability of NOT watching a dance challenge if the probability of watching one is 0.7?

Accepted Answer

$$1 - 0.7 = 0.3$$

Question 10

If you randomly select one person from a group of 6, where 2 are wearing hats, what is the probability of selecting someone with a hat?

Accepted Answer

$$\frac{2}{6} = 0.33$$

Question 11

Which of the following is TRUE about parametric tests?

Accepted Answer

They assume the data is normally distributed.

Question 12

What does the area under the curve of a probability density function represent?

Accepted Answer

The probability of all possible outcomes, which must sum to 1.

Question 13

If $$P(A) = 0.4$$ and $$P(B) = 0.5$$, and A and B are independent, what is $$P(A 	ext{ and } B)$$?

Accepted Answer

$$0.4 	imes 0.5 = 0.2$$

Question 14

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

Accepted Answer

It is always skewed.

Question 15

What is the formula for calculating a z-score?

Accepted Answer

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

Question 16

If the probability of watching a dog video is 0.1, and you watch 50 videos, how many would you expect to be about dogs?

Accepted Answer

$$0.1 	imes 50 = 5$$

Question 17

Which of the following is an example of a non-parametric test?

Accepted Answer

Chi-squared

Question 18

If you want to find the probability of a value being greater than 6 in a continuous normal distribution, what do you need to calculate?

Accepted Answer

The area under the curve to the right of 6.

Question 19

Which of the following statements about standardizing a distribution is TRUE?

Accepted Answer

Standardizing a distribution does not change its shape.

Question 20

If you have a discrete variable representing year of study, how do you find $$P(x \u003c 3)$$?

Accepted Answer

Sum the probabilities for year 1 and year 2.

The Normal Distribution & Probability: Core Concepts for Statistics

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