Question 1

A veterinarian records the weights of cats treated at a clinic. The weights 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 $$1.5$$?

Accepted Answer

$$x = 12$$ pounds

Question 2

The scores for the California Peace Officer Standards and Training test are normally distributed with a mean of $$50$$ and a standard deviation of $$10. $$What is the lowest score an applicant can earn to be in the top $$10\% of $$all scores?

Accepted Answer

$$63$$

Question 3

Suppose the mean annual rate of return for large growth mutual funds is $$21.2\%$$ with a standard deviation of $$3.5\%. $$Assuming normality, between what two values does the middle $$90\% of $$the data lie?

Accepted Answer

$$15.44\%$$ and $$26.96\%$$

Question 4

A researcher finds that the braking distances of cars from $$60$$ mph to a complete stop are normally distributed with a mean of $$131$$ feet and a standard deviation of $$6.14$$ feet. What is the longest braking distance that would still be in the bottom $$1\%$$?

Accepted Answer

$$117.7$$ feet

Question 5

In a randomly selected sample of U.S. adults ages $$20$$ and over, the mean total cholesterol level is $$187 mg/dL $$with 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

$$117.2 mg/dL$$

Question 6

The lengths of time employees have worked at a corporation are normally distributed with a mean of $$11.2$$ years and a standard deviation of $$2.1$$ years. If the lowest $$10\% in $$seniority are laid off, what is the maximum length of time an employee could have worked and still be laid off?

Accepted Answer

$$8.5$$ years

Question 7

Given a normal distribution with mean $$\mu = 52$$ and standard deviation $$\sigma = 15$$, what is the weight $$x$$ corresponding to a $$z-$$score of $$-1.2$$?

Accepted Answer

$$x = 34$$ pounds

Question 8

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

Accepted Answer

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

Question 9

If the area to the left of a $$z-$$score is $$0.9$$, what is the corresponding $$z-$$score (rounded to two decimal places)?

Accepted Answer

$$z = 1.28$$

Question 10

A cholesterol screening program wants to identify the top $$5\% of $$adults with the highest cholesterol levels. If the mean is $$190 mg/dL $$and the standard deviation is $$40.9 mg/dL$$, what is the minimum cholesterol level to be in the top $$5\%$$?

Accepted Answer

$$257.3 mg/dL$$

Question 11

A mutual fund's annual return is normally distributed with mean $$\mu = 0.212$$ and standard deviation $$\sigma = 0.035. $$What is the $$z-$$score for a return of $$0.28$$?

Accepted Answer

$$z = 1.94$$

Question 12

A test score is $$1.5$$ standard deviations below the mean. If the mean is $$50$$ and the standard deviation is $$10$$, what is the test score?

Accepted Answer

$$35$$

Question 13

If $$z = -2.33$$ corresponds to the $$1st $$percentile in a standard normal distribution, what is the $$x-$$value for a distribution with $$\mu = 187$$ and $$\sigma = 41.1$$?

Accepted Answer

$$x = 91.2$$

Question 14

A company wants to reward the top $$2.5\% of $$employees based on years worked. If the mean is $$11.2$$ years and the standard deviation is $$2.1$$ years, what is the minimum number of years to be in the top $$2.5\%$$?

Accepted Answer

$$15.6$$ years

Question 15

Which of the following best describes the interpretation of a $$z-$$score of $$0 in a $$normal distribution?

Accepted Answer

The value is equal to the mean.

Question 16

A veterinarian finds that the weights of dogs are normally distributed with mean $$52$$ pounds and standard deviation $$15$$ pounds. What is the weight corresponding to a $$z-$$score of $$2$$?

Accepted Answer

$$82$$ pounds

Question 17

If the area to the left of a $$z-$$score is $$0.01$$, what is the corresponding $$z-$$score?

Accepted Answer

$$z = -2.33$$

Question 18

A test score is $$1.96$$ standard deviations above the mean. If the mean is $$50$$ and the standard deviation is $$10$$, what is the test score?

Accepted Answer

$$69.6$$

Question 19

Which of the following statements is true about the area under the normal curve between $$z = -1.645$$ and $$z = 1.645$$?

Accepted Answer

It contains approximately $$90\% of $$the data.

Normal Probability Distributions: Finding Data Values and Percentiles

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