Q: A company will only hire applicants who score in the top 5% on a test that is normally distributed with a mean of 80 and a standard deviation of 6. What is the minimum score required to be eligible for hire?

$$x = 80 + 1.645 \times 6 = 89.87$$

Q: The cholesterol levels of adults are normally distributed with a mean of 187 mg/dL and a standard deviation of 41.1 mg/dL. What is the highest cholesterol level an adult can have and still be in the bottom 1%?

$$x = 187 + (-2.33) \times 41.1 \approx 91$$

Q: A hospital wants to identify patients in the lowest 2.5% of blood pressure readings. If the readings are normally distributed with a mean of 120 mmHg and a standard deviation of 15 mmHg, what is the maximum blood pressure for this group?

$$x = 120 + (-1.96) \times 15 = 90.6$$

Q: A normal distribution has a mean of 70 and a standard deviation of 8. What is the x-value corresponding to the 75th percentile?

$$x = 70 + 0.674 \times 8 = 75.39$$

Question 1

Suppose the weights of cats at a veterinary clinic are normally distributed with a mean of 9 pounds and a standard deviation of 2 pounds. What is the weight corresponding to a z-score of $$z = 1.5$$?

Accepted Answer

$$x = 12$$ pounds$

Question 2

A standardized test has scores that are normally distributed with a mean of 100 and a standard deviation of 15. What is the z-score for a student who scored 130?

Accepted Answer

$$z = 2$$

Question 3

Find the z-score that corresponds to the 95th percentile of the standard normal distribution.

Accepted Answer

$$z \approx 1.65$$

Question 4

If the area to the left of a z-score is 0.25, what is the z-score?

Accepted Answer

$$z \approx -0.67$$

Question 5

A company will only hire applicants who score in the top 5% on a test that is normally distributed with a mean of 80 and a standard deviation of 6. What is the minimum score required to be eligible for hire?

Accepted Answer

$$x = 80 + 1.645 	imes 6 = 89.87$$

Question 6

If the cumulative area to the left of a z-score is 0.80, what is the z-score?

Accepted Answer

$$z \approx 0.84$$

Question 7

The cholesterol levels of adults are normally distributed with a mean of 187 mg/dL and a standard deviation of 41.1 mg/dL. What is the highest cholesterol level an adult can have and still be in the bottom 1%?

Accepted Answer

$$x = 187 + (-2.33) 	imes 41.1 \approx 91$$

Question 8

Which formula is used to convert a z-score to an x-value in a normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$x = \mu + z \sigma$$

Question 9

A hospital wants to identify patients in the lowest 2.5% of blood pressure readings. If the readings are normally distributed with a mean of 120 mmHg and a standard deviation of 15 mmHg, what is the maximum blood pressure for this group?

Accepted Answer

$$x = 120 + (-1.96) 	imes 15 = 90.6$$

Question 10

If a z-score is 0, what does this indicate about the corresponding x-value in a normal distribution?

Accepted Answer

The x-value is equal to the mean $$\mu$$

Question 11

A student’s exam score corresponds to a z-score of $$-1.28. $$What percentage of students scored lower than this student?

Accepted Answer

10%

Question 12

Which of the following best describes the process for finding a z-score given a cumulative area under the normal curve?

Accepted Answer

Locate the area in the body of the Standard Normal Table and use the corresponding row and column to find the z-score

Question 13

If the area to the right of a z-score is 0.1075, what is the cumulative area to the left?

Accepted Answer

0.8925

Question 14

A normal distribution has a mean of 70 and a standard deviation of 8. What is the x-value corresponding to the 75th percentile?

Accepted Answer

$$x = 70 + 0.674 	imes 8 = 75.39$$

Question 15

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

Accepted Answer

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

Normal Probability Distributions: Finding Values and Applications

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