Q: A university wants to admit only the top 10% of students based on a normally distributed entrance exam with mean 500 and standard deviation 100. What is the minimum score a student must achieve to be admitted?

$$x = 500 + (1.645 \times 100) = 664.5$$

Q: Which Excel function would you use to find the probability that a value from a normal distribution is less than or equal to $$x$$?

$$\text{NORM.DIST}(x, \mu, \sigma, \text{TRUE})$$

Q: If the first quartile (25th percentile) of a normal distribution is needed, which Excel function and parameters should be used?

$$\text{NORM.INV}(0.25, \mu, \sigma)$$

Q: A hospital finds that the weights of newborns are normally distributed with a mean of 7.5 lbs and a standard deviation of 1.2 lbs. What weight marks the 90th percentile?

$$x = 7.5 + (1.28 \times 1.2) = 9.036$$

Q: A researcher wants to find the value $$x$$ such that only 5% of the population is above $$x in a $$normal distribution with mean 100 and standard deviation 15. What is $$x$$?

$$x = 100 + (1.645 \times 15) = 124.675 ($$but since 5% is above, use negative z: $$x = 100 + (-1.645 \times 15) = 75.325)$$

Question 1

Suppose the heights of adult women are normally distributed with a mean of 63.8 inches and a standard deviation of 2.6 inches. What is the $$z-$$score for a woman who is 68 inches tall?

Accepted Answer

$$z = \frac{68 - 63.8}{2.6} = 1.615$$

Question 2

A bag of potato chips is labeled as 12 ounces. The actual weights are normally distributed with a mean of 12 ounces and a standard deviation of 0.56 ounces. What is the probability that a randomly selected bag weighs more than 13 ounces?

Accepted Answer

About 4.78%

Question 3

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

Accepted Answer

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

Question 4

If the area to the left of $$z is 0.80 in a $$standard normal distribution, what is the approximate value of $$z$$?

Accepted Answer

$$z \approx 0.84$$

Question 5

A university wants to admit only the top 10% of students based on a normally distributed entrance exam with mean 500 and standard deviation 100. What is the minimum score a student must achieve to be admitted?

Accepted Answer

$$x = 500 + (1.645 	imes 100) = 664.5$$

Question 6

Which Excel function would you use to find the probability that a value from a normal distribution is less than or equal to $$x$$?

Accepted Answer

$$	ext{NORM.DIST}(x, \mu, \sigma, 	ext{TRUE})$$

Question 7

If the first quartile (25th percentile) of a normal distribution is needed, which Excel function and parameters should be used?

Accepted Answer

$$	ext{NORM.INV}(0.25, \mu, \sigma)$$

Question 8

A hospital finds that the weights of newborns are normally distributed with a mean of 7.5 lbs and a standard deviation of 1.2 lbs. What weight marks the 90th percentile?

Accepted Answer

$$x = 7.5 + (1.28 	imes 1.2) = 9.036$$

Question 9

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

Accepted Answer

The total area under the normal curve is always 1.

Question 10

A company wants to know what percentage of its products fall within one standard deviation of the mean in a normal distribution. What is the correct percentage?

Accepted Answer

About 68%

Question 11

If $$z = 2 in a $$standard normal distribution, what is the area to the left of $$z$$?

Accepted Answer

0.9772

Question 12

A researcher wants to find the value $$x$$ such that only 5% of the population is above $$x in a $$normal distribution with mean 100 and standard deviation 15. What is $$x$$?

Accepted Answer

$$x = 100 + (1.645 	imes 15) = 124.675 ($$but since 5% is above, use negative z: $$x = 100 + (-1.645 	imes 15) = 75.325)$$

Question 13

Which of the following best describes the difference between a standard normal distribution and a nonstandard normal distribution?

Accepted Answer

A standard normal distribution has a mean of 0 and a standard deviation of 1, while a nonstandard normal distribution can have any mean and standard deviation.

Question 14

If the probability that a randomly selected value from a normal distribution is less than $$x is 0.25$$, what is the $$z-$$score for $$x$$?

Accepted Answer

$$z = -0.674$$

Question 15

A certain chemical reaction time is normally distributed with mean 30 seconds and standard deviation 4 seconds. What is the probability that a randomly selected reaction takes less than 26 seconds?

Accepted Answer

0.1587

Applications of the Normal Distribution

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