Question 1

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

Accepted Answer

The normal distribution is symmetric about its mean.

Question 2

A random variable $$X is $$normally distributed with mean $$\mu = 50$$ and standard deviation $$\sigma = 10. $$What is the $$z-$$score for $$x = 70$$?

Accepted Answer

$$z = 2$$

Question 3

Which of the following best describes the Empirical Rule for a normal distribution?

Accepted Answer

All of the above.

Question 4

If $$X \sim N(100, 15)$$, what is the probability that $$X = 100$$?

Accepted Answer

0

Question 5

Which of the following is NOT a property of the probability density function (pdf) for a continuous random variable?

Accepted Answer

The pdf gives the probability that $$X$$ equals a specific value.

Question 6

A standardized test has scores that are normally distributed with mean $$\mu = 500$$ and standard deviation $$\sigma = 100. $$What is the $$z-$$score for a student who scored 650?

Accepted Answer

$$z = 1.5$$

Question 7

Which of the following statements about the cumulative distribution function (cdf) is correct?

Accepted Answer

The cdf is used to find the area under the curve to the left of a value.

Question 8

Suppose the heights of adult men are normally distributed with mean $$\mu = 70$$ inches and standard deviation $$\sigma = 3$$ inches. What percentage of men are expected to have heights between 67 and 73 inches?

Accepted Answer

About 68%

Question 9

If $$X is a $$continuous random variable, which of the following is always true?

Accepted Answer

$$P(X = c) = 0$$ for any constant $$c$$

Question 10

A pharmaceutical company finds that the time it takes for a drug to be absorbed into the bloodstream is normally distributed with mean $$\mu = 30$$ minutes and standard deviation $$\sigma = 5$$ minutes. What is the probability that a randomly selected patient absorbs the drug in less than 25 minutes?

Accepted Answer

About 16%

Question 11

Which of the following is the correct formula for converting a value $$x$$ from a normal distribution with mean $$\mu$$ and standard deviation $$\sigma to a$$ $$z-$$score?

Accepted Answer

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

Question 12

A quality control engineer is checking the weights of cereal boxes, which are normally distributed with mean $$\mu = 500g $$and $$\sigma = 10g. $$What is the probability that a box weighs more than 520g?

Accepted Answer

About 2.5%

Question 13

Which of the following best describes the area under the normal curve between $$\mu - 2\sigma$$ and $$\mu + 2\sigma$$?

Accepted Answer

About 95% of the data

Question 14

If a normal distribution has mean $$\mu = 0$$ and standard deviation $$\sigma = 1$$, what is this distribution called?

Accepted Answer

Standard normal distribution

Question 15

A researcher wants to find $$P(X \u003e x)$$ for a normal distribution. Which of the following is the correct approach?

Accepted Answer

$$P(X \u003e x) = 1 - P(X \u003c x)$$

Question 16

Which of the following is a correct interpretation of the phrase 'at least' in probability inequalities?

Accepted Answer

$$P(X \geq c)$$

Question 17

A hospital records the time (in minutes) it takes for patients to recover from anesthesia. The times are normally distributed with mean $$\mu = 40$$ and $$\sigma = 8. $$What is the $$z-$$score for a patient who recovers in 56 minutes?

Accepted Answer

$$z = 2$$

Question 18

Which of the following is TRUE about the area under the normal curve?

Accepted Answer

It represents the probability for intervals of $$x$$ values.

Question 19

A university finds that the average GPA of its students is normally distributed with mean $$\mu = 3.0$$ and $$\sigma = 0.4. $$What percentage of students have a GPA between 2.6 and 3.4?

Accepted Answer

About 68%

Question 20

Which of the following is the best definition of a continuous probability distribution?

Accepted Answer

A distribution where the probability of any single value is zero, but the probability over an interval is positive.

Normal Distribution: Properties and Applications

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