Q: Given a normal distribution with mean $$\mu = 400.3$$ feet and standard deviation $$\sigma = 25.6$$ feet, what is the 90th percentile distance for home runs?

$$x = 400.3 + (1.28 \times 25.6) = 432.1$$ feet$

Q: A binomial experiment with $$n = 200$$ and $$p = 0.085 is $$being considered for normal approximation. Is the normal approximation appropriate?

Yes, because $$np(1-p) = 200 \times 0.085 \times 0.915 = 15.55 \geq 10$$

Question 1

Suppose the time (in minutes) it takes for a package to be delivered by UPS is uniformly distributed between 0 and 60 minutes. What is the probability that a package arrives between 10:15 am and 10:30 am (i.e., between 15 and 30 minutes after 10 am)?

Accepted Answer

$$\frac{15}{60} = 0.25$$

Question 2

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

Accepted Answer

The area under the curve is always less than 1.

Question 3

If the mean $$\mu of a $$normal distribution is increased while keeping the standard deviation $$\sigma$$ constant, what happens to the graph of the normal curve?

Accepted Answer

The curve shifts to the right along the x-axis.

Question 4

According to the Empirical Rule, approximately what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

$$95\%$$

Question 5

A factory produces ball bearings with diameters that are normally distributed with mean $$\mu = 1 cm $$and standard deviation $$\sigma = 0.002 cm. $$What is the z-score for a ball bearing with a diameter of $$0.995 cm$$?

Accepted Answer

$$z = \frac{0.995 - 1}{0.002} = -2.5$$

Question 6

If the area under a normal curve to the right of $$x = 450$$ feet is $$0.026$$, what does this mean in the context of home run distances?

Accepted Answer

2.6% of home runs traveled more than 450 feet.

Question 7

Given a normal distribution with mean $$\mu = 400.3$$ feet and standard deviation $$\sigma = 25.6$$ feet, what is the 90th percentile distance for home runs?

Accepted Answer

$$x = 400.3 + (1.28 	imes 25.6) = 432.1$$ feet$

Question 8

Which of the following statements about normal probability plots is TRUE?

Accepted Answer

If the plot is approximately linear, the data may be normally distributed.

Question 9

A binomial experiment with $$n = 200$$ and $$p = 0.085 is $$being considered for normal approximation. Is the normal approximation appropriate?

Accepted Answer

Yes, because $$np(1-p) = 200 	imes 0.085 	imes 0.915 = 15.55 \geq 10$$

Question 10

For a normal distribution, what is the probability that a randomly selected value is more than three standard deviations above the mean?

Accepted Answer

$$0.0015$$

Question 11

If a normal probability plot for a sample of size $$n = 15$$ has a correlation coefficient of $$0.935$$, what can you conclude using Table VI?

Accepted Answer

The data may not be normally distributed because $$0.935 \u003c 0.939.$$

Question 12

A random variable $$X is $$uniformly distributed on the interval $$[0, 60]. $$What is the probability that $$X is $$less than 20?

Accepted Answer

$$\frac{20}{60} = 0.333$$

Question 13

Which of the following best describes the role of area under the normal curve between two values $$a$$ and $$b$$?

Accepted Answer

It represents the probability that a randomly selected value falls between $$a$$ and $$b.$$

Question 14

If the standard deviation $$\sigma of a $$normal distribution increases while the mean $$\mu$$ stays the same, what happens to the normal curve?

Accepted Answer

The curve becomes wider and shorter.

Question 15

A normal distribution has mean $$\mu = 100$$ and standard deviation $$\sigma = 15. $$What is the probability that a randomly selected value is between $$85$$ and $$115$$?

Accepted Answer

Approximately $$68\%$$

Question 16

Which of the following is a criterion for a binomial probability experiment?

Accepted Answer

Each trial has only two possible outcomes.

Chapter 7: The Normal Probability Distribution – Structured Study Notes

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