Q: The distribution of heights of college-aged males is approximately normal with mean 70 inches and standard deviation 2.3 inches. Between which heights do the middle 99.7% of students fall?

Between $$70 - 3 \times 2.3$$ and $$70 + 3 \times 2.3$$ inches

Question 1

Which of the following best describes a discrete variable?

Accepted Answer

A variable whose possible values are countable and distinct, such as the number of students in a class.

Question 2

Which equation represents the probability density function (PDF) for a normal distribution with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$f(x) = \frac{1}{\sigma \sqrt{2\pi}} e$$^{-\frac{(x-\mu)^2}$${2\$$sigma^2$$}}$$

Question 3

The distribution of heights of college-aged males is approximately normal with mean 70 inches and standard deviation 2.3 inches. Between which heights do the middle 99.7% of students fall?

Accepted Answer

Between $$70 - 3 	imes 2.3$$ and $$70 + 3 	imes 2.3$$ inches

Question 4

Which of the following is NOT a property of a probability density function (PDF)?

Accepted Answer

The function can take negative values for some $$x.$$

Question 5

ACT scores in Ohio are normally distributed with mean 22 and standard deviation 4.5. What percent of Ohio students will have an ACT score less than 15?

Accepted Answer

About 5%

Question 6

Which formula would you use to convert a raw score $$x to a$$ $$z-$$score in a normal distribution?

Accepted Answer

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

Question 7

Birth weights of medium breed puppies are normally distributed with mean 250 grams and standard deviation 55 grams. What is the probability that a puppy is born with a low birth weight (less than 150 grams)?

Accepted Answer

About 2.5%

Question 8

Which of the following best describes a continuous variable?

Accepted Answer

A variable whose possible values are uncountable and can take any value within an interval.

Question 9

If ACT scores are normally distributed with mean 22 and standard deviation 4.5, what is the lowest possible score to qualify for the top 10%?

Accepted Answer

About 28.8

Question 10

A uniform distribution is defined by which of the following properties?

Accepted Answer

All outcomes in the interval are equally likely.

Question 11

Birth weights of medium breed puppies are normally distributed with mean 250 grams and standard deviation 55 grams. What is the least a puppy would weigh if it was in the top 10% of birth weights?

Accepted Answer

About 321 grams

Question 12

Which of the following statements about the normal distribution is FALSE?

Accepted Answer

The total area under the curve is less than 1.

Question 13

If the probability that a puppy weighs more than 350 grams is required, which calculation should be performed?

Accepted Answer

Find the $$z-$$score for 350 grams and use the normal distribution table to find $$P(X \u003e 350).$$

Question 14

Which formula gives the probability for a value $$x in a $$uniform distribution from $$a to$$ $$b$$?

Accepted Answer

$$P(x) = \frac{1}{b-a}$$ for $$a \leq x \leq b$$

Question 15

ACT scores in Ohio are normally distributed with mean 22 and standard deviation 4.5. What percent of Ohio students will have an ACT score between 20 and 31?

Accepted Answer

About 70%

Question 16

Which of the following is the most a puppy would weigh if it was in the bottom 10% of birth weights (mean 250g, SD 55g)?

Accepted Answer

About 179 grams

Question 17

Which scenario best illustrates the use of a continuous variable?

Accepted Answer

Measuring the exact time (in seconds) it takes for a chemical reaction to complete.

Question 18

If the mean ACT score is 22 and the standard deviation is 4.5, what is the $$z-$$score for a student who scored 31?

Accepted Answer

$$z = \frac{31 - 22}{4.5} = 2$$

Normal Distributions, Probability, and Key Statistical Concepts – Guided Review

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