Q: A veterinarian wants to know what weight corresponds to the 90th percentile for dogs, given a mean of 52 pounds and a standard deviation of 15 pounds. What is the correct formula to use?

$$x = 52 + z_{0.90} \times 15$$

Question 1

Given a cumulative area of 0.3632 under the standard normal curve, what is the corresponding z-score?

Accepted Answer

$$z = -0.35$$

Question 2

A hospital administrator wants to know the minimum test score required to be in the top 10.75% of applicants. What z-score should she use to determine this cutoff?

Accepted Answer

$$z = 1.24$$

Question 3

Which formula correctly transforms a z-score to an x value in a normal distribution?

Accepted Answer

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

Question 4

The weights of dogs at a clinic are normally distributed with a mean of 52 pounds and a standard deviation of 15 pounds. What is the weight corresponding to a z-score of 3?

Accepted Answer

$$x = 97$$ pounds

Question 5

If the lowest 10% of employees (by years of service) are to be laid off, and years of service are normally distributed with mean 11.2 years and standard deviation 2.1 years, what is the maximum number of years an employee could have worked and still be laid off?

Accepted Answer

$$x = 8.509$$ years

Question 6

Which of the following best describes the meaning of a z-score of $$-2.33 in a $$normal distribution?

Accepted Answer

The value is 2.33 standard deviations below the mean.

Question 7

A student’s test score corresponds to the 10th percentile in a normal distribution. What is the z-score for this percentile?

Accepted Answer

$$z = -1.282$$

Question 8

If a z-score is 0.58, the mean is 52, and the standard deviation is 15, what is the corresponding x value?

Accepted Answer

$$x = 60.7$$

Question 9

A company wants to reward employees in the top 5% of years of service. If years of service are normally distributed with mean 11.2 years and standard deviation 2.1 years, what is the minimum z-score an employee must have to be in the top 5%?

Accepted Answer

$$z = 1.645$$

Question 10

Which of the following steps is necessary when using a standard normal table to find a z-score for a given area to the right of a value?

Accepted Answer

Subtract the area from 1 to get the cumulative probability to the left.

Question 11

A veterinarian wants to know what weight corresponds to the 90th percentile for dogs, given a mean of 52 pounds and a standard deviation of 15 pounds. What is the correct formula to use?

Accepted Answer

$$x = 52 + z_{0.90} 	imes 15$$

Question 12

If the cumulative probability to the left of a value is 0.8925, what is the area to the right of that value under the standard normal curve?

Accepted Answer

$$0.1075$$

Question 13

A company’s employee tenure is normally distributed with mean 11.2 years and standard deviation 2.1 years. What is the z-score for an employee who has worked 13.3 years?

Accepted Answer

$$z = 1.0$$

Question 14

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

Accepted Answer

The mean is 0 and the standard deviation is 1.

Question 15

A student finds a z-score of $$-1.282$$ for a test score. What percentile does this correspond to?

Accepted Answer

10th percentile

Question 16

If a value is 0.58 standard deviations above the mean in a normal distribution, which of the following is true?

Accepted Answer

Its z-score is 0.58.

Question 17

A researcher wants to find the x value that corresponds to the 25th percentile in a normal distribution with mean $$\mu$$ and standard deviation $$\sigma. $$Which z-score should be used?

Accepted Answer

$$z = -0.674$$

Question 18

Which of the following is the correct interpretation of a cumulative probability in the context of the standard normal distribution?

Accepted Answer

It is the probability that a value is less than or equal to a given z-score.

Question 19

If a cumulative probability is not found exactly in the z-table, what is the best approach to estimate the corresponding z-score?

Accepted Answer

Use the closest probability in the table and interpolate if necessary.

Finding Z-Scores and Data Values in the Normal Distribution

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