Q: Which Desmos command would you use to find the 95th percentile of a normal distribution with mean 63.7 and standard deviation 2.9?

$$\text{inversecdf(normaldist(63.7, 2.9), 0.95)}$$

Question 1

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

Accepted Answer

The total area under the curve is less than 1.

Question 2

Suppose the heights of men are normally distributed with mean $$\mu = 68.6 in. $$and standard deviation $$\sigma = 2.8 in. $$What is the probability that a randomly selected man is taller than 72 inches?

Accepted Answer

About 0.112 or 11.2%

Question 3

A normal distribution with mean $$\mu = 0$$ and standard deviation $$\sigma = 1 is $$called:

Accepted Answer

The standard normal distribution

Question 4

If $$X \sim N(63.7, 2.9)$$, what is the probability that $$64 \leq X \leq 77$$? (Use the Desmos result shown in the study material.)

Accepted Answer

0.459

Question 5

Which Desmos command would you use to find the 95th percentile of a normal distribution with mean 63.7 and standard deviation 2.9?

Accepted Answer

$$	ext{inversecdf(normaldist(63.7, 2.9), 0.95)}$$

Question 6

A company wants to design a cockpit to accommodate the shortest 95% of women. If heights are normally distributed with $$\mu = 63.7 in. $$and $$\sigma = 2.9 in$$., what is the maximum allowable height for the cockpit?

Accepted Answer

68.47 inches

Question 7

Which of the following best describes a normal quantile (probability) plot for a dataset that is approximately normally distributed?

Accepted Answer

The points lie roughly on a straight line.

Question 8

Pulse rates of women are normally distributed with mean $$\mu = 74.0$$ and $$\sigma = 12.5. $$What pulse rate marks the lowest 5% of women?

Accepted Answer

53.44 beats per minute

Question 9

Which of the following statements about the Empirical Rule for normal distributions is correct?

Accepted Answer

About 68% of the data falls within one standard deviation of the mean.

Question 10

If a dataset's normal quantile plot shows a strong S-shaped pattern, what does this indicate?

Accepted Answer

The data is not normally distributed.

Question 11

Given $$X \sim N(74.0, 12.5)$$, what pulse rate marks the highest 5% of women?

Accepted Answer

94.56 beats per minute

Question 12

Which of the following is the correct notation for a normal random variable with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$X \sim N(\mu, \sigma)$$

Question 13

A histogram of electricity rates is strongly skewed right. What does this suggest about the underlying distribution?

Accepted Answer

It is not normally distributed.

Question 14

If $$Z is a $$standard normal variable, what does a z-score of 1.21 mean?

Accepted Answer

The value is 1.21 standard deviations above the mean.

Question 15

Which of the following real-world scenarios is most likely to be modeled by a normal distribution?

Accepted Answer

Heights of adult women in a large population

Question 16

If the area to the right of $$x = 72 in a $$normal distribution with $$\mu = 68.6$$ and $$\sigma = 2.8 is 0.112$$, what does this area represent?

Accepted Answer

The probability that a randomly selected value is greater than 72.

Question 17

Which of the following best explains why the normal distribution is important in statistics?

Accepted Answer

Many real-world phenomena are approximately normally distributed.

Real Applications of the Normal Distribution

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