Question 1

Which of the following is NOT a property of the normal density curve?

Accepted Answer

The mean, median, and mode are all equal.

Question 2

A random variable $$X is $$uniformly distributed between 0 and 60. What is the probability that $$X$$ falls between 15 and 30?

Accepted Answer

$$\frac{30}{60} = 0.5$$

Question 3

If the mean diameter of ball bearings is 1 cm and the standard deviation is 0.002 cm, what proportion of ball bearings are expected to have diameters between 0.995 cm and 1.005 cm?

Accepted Answer

Approximately 95%

Question 4

Which equation represents the standard deviation of a binomial random variable $$X$$ with $$n$$ trials and probability $$p of $$success?

Accepted Answer

$$\sigma = \sqrt{np(1-p)}$$

Question 5

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

Accepted Answer

95%

Question 6

If a normal random variable $$X$$ has mean $$\mu = 400.3$$ and standard deviation $$\sigma = 25.6$$, what is the $$z-$$score for a home run that traveled 450 feet?

Accepted Answer

$$z = \frac{450 - 400.3}{25.6}$$

Question 7

A normal probability plot is used to assess normality. If the plot is approximately linear, what does this indicate?

Accepted Answer

The data could come from a population that is normally distributed.

Question 8

For a binomial experiment with $$n = 100$$ and $$p = 0.0323$$, is the normal approximation appropriate?

Accepted Answer

Yes, because $$np(1-p) \geq 10$$

Question 9

If the area under the normal curve to the right of $$x = 450$$ feet is $$0.026$$, what does this mean?

Accepted Answer

2.6% of home runs traveled more than 450 feet.

Question 10

What is the formula for the expected proportion of observations less than or equal to the $$ith $$data value in a normal probability plot?

Accepted Answer

$$f_i = \frac{i-0.375}{n+0.25}$$

Question 11

If a normal random variable $$X$$ has mean $$\mu = 1$$ and standard deviation $$\sigma = 0.002$$, what is the probability that $$X is $$less than $$0.999$$?

Accepted Answer

Find the area under the normal curve to the left of $$x = 0.999$$ using $$z = \frac{0.999 - 1}{0.002}$$

Question 12

Which of the following statements about the normal curve is TRUE?

Accepted Answer

The area under the curve to the left of the mean equals the area to the right of the mean.

Question 13

If the linear correlation coefficient for a normal probability plot is greater than the critical value in Table VI, what can you conclude?

Accepted Answer

The data is approximately normal.

Question 14

A home run distance is at the 90th percentile in a normal distribution with $$\mu = 400.3$$ and $$\sigma = 25.6. $$What is the distance?

Accepted Answer

$$x = \mu + z_{0.90} \cdot \sigma$$

Question 15

For a binomial experiment with $$n = 200$$ and $$p = 0.085$$, what is the expected number of households buying a pet dog a gift?

Accepted Answer

$$200 	imes 0.085 = 17$$

Question 16

Which of the following best describes the role of area under a normal curve?

Accepted Answer

It represents the probability of observing a value in a given interval.

Question 17

If a histogram of sample data is symmetric and bell-shaped, what can you infer about the underlying population?

Accepted Answer

The population is likely to be normally distributed.

Question 18

What is the probability that a randomly selected value from a normal distribution falls more than three standard deviations from the mean?

Accepted Answer

Approximately 0.3%

Question 19

If the mean, median, and mode of a distribution are all equal, which type of distribution is most likely being described?

Accepted Answer

Normal distribution

Question 20

Which of the following is a criterion for using the normal approximation to the binomial distribution?

Accepted Answer

$$np(1-p) \geq 10$$

Chapter 7: The Normal Probability Distribution – Study Notes

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