Q: Given a normal distribution with mean $$\mu = 172$$ and standard deviation $$\sigma = 29$$, which calculator function would you use to find the probability that a randomly selected man weighs less than 174 pounds?

$$\text{normalcdf}(-10$$^{99}$$, 174, 172, 29)$$

Q: If you want to find the weight that separates the lightest $$99.5\% of $$men from the heaviest $$0.5\%$$, which calculator function should you use?

$$\text{invNorm}(0.995, 172, 29)$$

Q: Which of the following is the correct formula for finding the probability that a normally distributed variable $$X is $$less than a value $$a$$?

$$P(X \u003c a) = \text{normalcdf}(-10$$^{99}$$, a, \mu, \sigma)$$

Question 1

Suppose the weights of adult men are normally distributed with a mean $$\mu = 172$$ pounds and a standard deviation $$\sigma = 29$$ pounds. What is the probability that a randomly selected man weighs less than 174 pounds?

Accepted Answer

$$0.5275$$

Question 2

Given a normal distribution with mean $$\mu = 172$$ and standard deviation $$\sigma = 29$$, which calculator function would you use to find the probability that a randomly selected man weighs less than 174 pounds?

Accepted Answer

$$	ext{normalcdf}(-10$$^{99}$$, 174, 172, 29)$$

Question 3

If you want to find the weight that separates the lightest $$99.5\% of $$men from the heaviest $$0.5\%$$, which calculator function should you use?

Accepted Answer

$$	ext{invNorm}(0.995, 172, 29)$$

Question 4

What is the weight that separates the lightest $$99.5\% of $$men from the heaviest $$0.5\% in a $$normal distribution with mean $$172$$ and standard deviation $$29$$?

Accepted Answer

$$247$$ pounds

Question 5

Which of the following best describes the area under the normal curve to the left of $$x = 174$$ when $$\mu = 172$$ and $$\sigma = 29$$?

Accepted Answer

It represents the probability that a randomly selected man weighs less than $$174$$ pounds.

Question 6

A hospital wants to set a weight limit for a new piece of equipment so that only the heaviest $$0.5\% of $$men would exceed it. What weight should they use as the cutoff?

Accepted Answer

$$247$$ pounds

Question 7

If the area to the left of a certain weight $$x$$ under a normal curve is $$0.995$$, what does $$x$$ represent?

Accepted Answer

The $$99.5th $$percentile

Question 8

Which of the following is the correct formula for finding the probability that a normally distributed variable $$X is $$less than a value $$a$$?

Accepted Answer

$$P(X \u003c a) = 	ext{normalcdf}(-10$$^{99}$$, a, \mu, \sigma)$$

Question 9

A researcher claims that $$52.75\% of $$men weigh less than $$174$$ pounds. If the weights are normally distributed with $$\mu = 172$$ and $$\sigma = 29$$, is this claim accurate?

Accepted Answer

Yes, because $$P(X \u003c 174) \approx 0.5275$$ for this distribution.

Question 10

If you use the $$z-$$table instead of a calculator to find $$P(X \u003c 174)$$ for $$\mu = 172$$ and $$\sigma = 29$$, what is the first step?

Accepted Answer

Calculate the $$z-$$score: $$z = \frac{174 - 172}{29}$$

Question 11

A company wants to know what percentage of men weigh more than $$247$$ pounds. What is the correct approach?

Accepted Answer

Calculate $$P(X \u003e 247) = 1 - P(X \u003c 247)$$

Question 12

If $$X is $$normally distributed with mean $$172$$ and standard deviation $$29$$, what is the $$z-$$score for $$x = 174$$?

Accepted Answer

$$z = \frac{174 - 172}{29} \approx 0.069$$

Question 13

Which of the following statements is TRUE about the normal distribution of men's weights with $$\mu = 172$$ and $$\sigma = 29$$?

Accepted Answer

About $$68\% of $$men's weights fall within one standard deviation of the mean.

Question 14

A gym wants to design equipment for men who weigh less than $$174$$ pounds. What percentage of men will be able to use this equipment?

Accepted Answer

$$52.75\%$$

Applications of the Normal Distribution in Statistics

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