Q: A newborn baby’s weight is normally distributed with $$\mu = 7$$ lbs and $$\sigma = 2.5$$ lbs. What weight separates the bottom 82% of babies from the top 18%?

$$7 + (0.92 \times 2.5) = 9.3$$ lbs

Question 1

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

Accepted Answer

Its mean is equal to 1.

Question 2

A bone mineral density test result is normally distributed with $$\mu = 0$$ and $$\sigma = 1. $$What is the probability that a randomly selected adult has a result less than $$z = 1.27$$?

Accepted Answer

About 0.8980

Question 3

If the area to the left of a certain $$z-$$score is 0.7542, what is the $$z-$$score?

Accepted Answer

$$z \approx 0.69$$

Question 4

Suppose women’s heights are normally distributed with $$\mu = 63.8$$ inches and $$\sigma = 2.6$$ inches. What percentage of women are at least 70 inches tall?

Accepted Answer

About 2.5%

Question 5

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

Accepted Answer

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

Question 6

A sample of 25 men is selected. Their weights are normally distributed with $$\mu = 172 lb $$and $$\sigma = 29 lb. $$What is the standard deviation of the sample mean?

Accepted Answer

$$\sigma_{\bar{x}} = \frac{29}{\sqrt{25}} = 5.8$$

Question 7

If the area to the left of $$z is 0.2222$$, what is the value of $$z$$?

Accepted Answer

$$z \approx -0.76$$

Question 8

A newborn baby’s weight is normally distributed with $$\mu = 7$$ lbs and $$\sigma = 2.5$$ lbs. What weight separates the bottom 82% of babies from the top 18%?

Accepted Answer

$$7 + (0.92 	imes 2.5) = 9.3$$ lbs

Question 9

Which calculator function would you use to find the area between two $$z-$$scores in the standard normal distribution?

Accepted Answer

normalcdf(L.B., U.B., 0, 1)

Question 10

A water taxi has a safe load of 3500 lb. If 25 men are randomly selected, each with a mean weight of 172 lb and $$\sigma = 29 lb$$, what is the probability their mean weight exceeds 175 lb?

Accepted Answer

Find $$z = \frac{175 - 172}{29/\sqrt{25}} = 0.52$$; probability is about 0.3015

Question 11

If the probability that a randomly selected value is less than $$z = -1.50 is $$needed, which of the following is closest to the correct probability?

Accepted Answer

0.0668

Question 12

The Central Limit Theorem states that for a sufficiently large sample size, the distribution of the sample mean will be:

Accepted Answer

Approximately normal, regardless of the population distribution

Question 13

An elevator has a maximum capacity of 16 passengers with a total weight of 2500 lb. If male weights are normally distributed with $$\mu = 182.9 lb $$and $$\sigma = 40.8 lb$$, what is the probability that the mean weight of 16 men exceeds 156.25 lb?

Accepted Answer

Find $$z = \frac{156.25 - 182.9}{40.8/\sqrt{16}} = -2.61$$; probability is about 0.9955

Question 14

Which of the following best describes an 'unusual' event in the context of the standard normal distribution?

Accepted Answer

An event with a $$z-$$score less than $$-2 or $$greater than $$2$$

Question 15

If the area to the left of $$z is 0.60$$, what is the $$z-$$score?

Accepted Answer

$$z \approx 0.25$$

Normal Probability Distributions and Their Applications

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