Question 1

Which of the following best describes the normal curve?

Accepted Answer

A bell-shaped curve that is unimodal, symmetric, and defined mathematically.

Question 2

Why does increasing the sample size make the sample distribution more closely resemble a normal curve?

Accepted Answer

Because the central limit theorem states that as sample size increases, the distribution of sample means approaches normality.

Question 3

Which of the following variables is most likely to be normally distributed?

Accepted Answer

Height of adult humans

Question 4

What is the formula for calculating a z score from a raw score $X$?

Accepted Answer

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

Question 5

A student scores 85 on a test where the mean is 75 and the standard deviation is 5. What is the student's z score?

Accepted Answer

$z = 2$

Question 6

If a z score is negative, what does this indicate about the raw score?

Accepted Answer

The raw score is below the mean.

Question 7

How do you convert a z score back into a raw score?

Accepted Answer

$X = z \sigma + \mu$

Question 8

Why is standardization useful in research?

Accepted Answer

It allows scores from different distributions to be compared directly.

Question 9

What does the area under the normal curve represent in the context of z scores?

Accepted Answer

The percentile rank or probability of a score occurring.

Question 10

According to the central limit theorem, what happens to the distribution of sample means as the sample size increases?

Accepted Answer

It becomes more normally distributed, regardless of the population's distribution.

Question 11

What is the formula for the standard error of the mean?

Accepted Answer

$\sigma_M = \frac{\sigma}{\sqrt{N}}$

Question 12

A researcher wants to compare test scores from two different exams with different means and standard deviations. What should they do?

Accepted Answer

Convert the raw scores to z scores for each exam.

Question 13

If a distribution is severely skewed, what happens to the distribution of sample means as sample size increases?

Accepted Answer

It becomes less skewed and approaches normality.

Question 14

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

Accepted Answer

It is always skewed to the left.

Question 15

A z score of 0 corresponds to which of the following?

Accepted Answer

A score equal to the mean.

Question 16

If the standard deviation of a population is 10 and the sample size is 25, what is the standard error of the mean?

Accepted Answer

$2$

Question 17

Which of the following statements about the distribution of means is TRUE?

Accepted Answer

Its standard deviation is less than the population standard deviation.

Question 18

A researcher finds a z score of 2.5 for a participant's test score. What does this mean?

Accepted Answer

The participant scored 2.5 standard deviations above the mean.

Question 19

Which formula should be used to calculate the z score for a sample mean $M$?

Accepted Answer

$z = \frac{M - \mu_M}{\sigma_M}$

The Normal Curve, Standardization, and z Scores

Study Guide - Practice Questions