Q: A student scores 1.5 standard deviations above the mean on a standardized test. If the mean score is 500 and the standard deviation is 100, what is the student's score?

$$500 + (1.5 \times 100) = 650$$

Q: If the mean of a normal distribution is 100 and the standard deviation is 20, what is the raw score corresponding to $$z = -1.5$$?

$$100 + (-1.5 \times 20) = 70$$

Question 1

Suppose a researcher is interested in the distribution of heights of adult males in a city. If the heights are normally distributed with a mean of 70 inches and a standard deviation of 3 inches, what is the z-score for a man who is 76 inches tall?

Accepted Answer

$$z = \frac{76 - 70}{3} = 2$$

Question 2

A hospital records the systolic blood pressure of its patients. The readings are normally distributed with a mean of 120 mmHg and a standard deviation of 15 mmHg. What percentage of patients have a systolic blood pressure between 105 mmHg and 135 mmHg?

Accepted Answer

Approximately 68%

Question 3

Which of the following statements about the standard normal distribution is TRUE?

Accepted Answer

It has a mean of 0 and a standard deviation of 1.

Question 4

A student scores 1.5 standard deviations above the mean on a standardized test. If the mean score is 500 and the standard deviation is 100, what is the student's score?

Accepted Answer

$$500 + (1.5 	imes 100) = 650$$

Question 5

If the area to the left of a z-score is 0.975, what is the corresponding z-score?

Accepted Answer

$$z \approx 1.96$$

Question 6

A pharmaceutical company claims that its drug is effective for 99% of patients. What is the z-score that corresponds to the top 1% of a standard normal distribution?

Accepted Answer

$$z \approx 2.33$$

Question 7

Which formula is used to convert a raw score $$x to a z-$$score in a normal distribution?

Accepted Answer

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

Question 8

A sample of exam scores is normally distributed with a mean of 80 and a standard deviation of 10. What score corresponds to the 84th percentile?

Accepted Answer

$$80 + (1 	imes 10) = 90$$

Question 9

A researcher finds that the z-score for a data value is -2.29. What does this indicate about the data value?

Accepted Answer

It is 2.29 standard deviations below the mean.

Question 10

If a value has a z-score of 0, what does this mean?

Accepted Answer

The value is equal to the mean.

Question 11

A company wants to know the probability that a randomly selected employee earns more than $$z = 1.28$$ standard deviations above the mean salary. What is this probability?

Accepted Answer

Approximately 10%

Question 12

Which of the following best describes the empirical rule for a normal distribution?

Accepted Answer

About 68% of data falls within one standard deviation of the mean.

Question 13

A psychologist is studying reaction times, which are normally distributed with a mean of 250 ms and a standard deviation of 30 ms. What is the probability that a randomly selected person has a reaction time less than 220 ms?

Accepted Answer

Approximately 5%

Question 14

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

Accepted Answer

It is skewed to the right.

Question 15

A test score is at the 97.5th percentile. What is the corresponding z-score?

Accepted Answer

$$z \approx 1.96$$

Question 16

If the mean of a normal distribution is 100 and the standard deviation is 20, what is the raw score corresponding to $$z = -1.5$$?

Accepted Answer

$$100 + (-1.5 	imes 20) = 70$$

Question 17

A university wants to award scholarships to students who score in the top 2.5% on an entrance exam. What is the minimum z-score a student must achieve?

Accepted Answer

$$z \approx 1.96$$

Question 18

Which of the following scenarios best illustrates the use of the normal distribution in real life?

Accepted Answer

Analyzing IQ scores of a large population.

Question 19

A value is 2 standard deviations above the mean in a normal distribution. What percentage of values are less than this value?

Accepted Answer

Approximately 97.5%

Question 20

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

Accepted Answer

It is less than the mean.

Chapter 9 Review: Hypothesis Testing for One Sample

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