Question 1

Which of the following best describes the total area under a density curve?

Accepted Answer

It is always equal to 1.

Question 2

A density curve is used to model the distribution of a population. What does the area under the curve between two values represent?

Accepted Answer

The proportion of individuals with values in that range.

Question 3

For a symmetric density curve, which of the following statements is true?

Accepted Answer

The mean and median are equal.

Question 4

The mean of a skewed density curve is:

Accepted Answer

Pulled in the direction of the long tail.

Question 5

Which formula represents the probability density function of a normal distribution?

Accepted Answer

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

Question 6

If a population is normally distributed with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, what percentage of the population falls between 85 and 115?

Accepted Answer

About 68%

Question 7

A student scores 1.8 standard deviations above the mean on a standardized test. What is their z-score?

Accepted Answer

$$z = 1.8$$

Question 8

Given a normal distribution $$N(270, 15)$$ for human pregnancy length, what is the z-score for a pregnancy lasting 240 days?

Accepted Answer

$$z = \frac{240 - 270}{15} = -2$$

Question 9

Which of the following is NOT a condition for using the normal model to describe a population?

Accepted Answer

The data must be bimodal.

Question 10

A QQ plot (Normal Probability Plot) is used to:

Accepted Answer

Assess whether a dataset is approximately normal.

Question 11

If the area under a normal curve to the left of $$z = -2.33 is 0.0099$$, what is the area to the right of $$z = 2.33$$?

Accepted Answer

0.0099

Question 12

A histogram of exam scores is bell-shaped and symmetric. Which statement is most accurate?

Accepted Answer

The mean and median are approximately equal.

Question 13

A researcher wants to know what proportion of pregnancies last between 255 and 300 days, given $$\mu = 270$$ and $$\sigma = 15. $$Which calculation should they perform?

Accepted Answer

Find the area under $$N(270, 15)$$ between $$x = 255$$ and $$x = 300.$$

Question 14

Which of the following best describes a z-score?

Accepted Answer

The number of standard deviations a value is from the mean.

Question 15

If a dataset is strongly skewed right, which of the following is most likely true?

Accepted Answer

The mean is greater than the median.

Question 16

A sample of heights is approximately normal with $$\mu = 64.5$$ inches and $$\sigma = 2.5$$ inches. What proportion of women are taller than 69.5 inches?

Accepted Answer

About 2.5%

Question 17

Which of the following is a correct interpretation of the 68-95-99.7 rule for normal distributions?

Accepted Answer

About 95% of data falls within 2 standard deviations of the mean.

Question 18

A student’s exam score has a z-score of $$-1.2. $$What does this mean?

Accepted Answer

The score is 1.2 standard deviations below the mean.

Question 19

Why is it important to check the Nearly Normal Condition before applying the normal model?

Accepted Answer

Because the normal model may not be appropriate for data that is not symmetric, unimodal, and without outliers.

Density Curves and the Normal Distribution: Study Notes for Introductory Statistics

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