Question 1

Which of the following statements about the normal curve is TRUE?

Accepted Answer

The area under the normal curve is equal to 1.

Question 2

What does the center of a normal curve represent?

Accepted Answer

The mean, median, and mode

Question 3

According to the Empirical Rule, approximately what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

$$95\%$$

Question 4

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

Accepted Answer

$$z = 2$$

Question 5

Which formula is used to calculate the $$z-$$score for a value $$x in a $$normal distribution?

Accepted Answer

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

Question 6

If the mean birth weight of full-term babies is $$3400$$ grams with a standard deviation of $$505$$ grams, what is the $$z-$$score for a baby weighing $$3905$$ grams?

Accepted Answer

$$z = 1$$

Question 7

Which of the following best describes the shape of the normal curve?

Accepted Answer

Symmetrical and bell-shaped

Question 8

A student scores 1.5 standard deviations above the mean on a normally distributed exam. What can you say about their percentile rank?

Accepted Answer

They are above the 50th percentile.

Question 9

If $$z = 0$$ for a value in a normal distribution, what does this indicate about the value?

Accepted Answer

It is at the mean.

Question 10

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

Accepted Answer

Most values are far from the mean.

Question 11

Suppose the reading speed of sixth grade students is normally distributed with mean $$125$$ words per minute and standard deviation $$24. $$What is the probability that a randomly selected student reads faster than $$140$$ words per minute?

Accepted Answer

About $$10\%$$

Question 12

If a value is at the 90th percentile of a normal distribution, what does this mean?

Accepted Answer

It is greater than 90% of all values.

Probability and Normal Distribution: Study Notes for Introductory Statistics

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