Question 1

Which statement best describes a normal random variable?

Accepted Answer

Its graph is symmetric about the mean.

Answer

It only takes whole number values.

Answer

It has values that increase uniformly.

Answer

It has more extreme values on one side.

Question 2

What is the shape of the probability distribution of a normal random variable?

Accepted Answer

Bell-shaped

Answer

Rectangular

Answer

U-shaped

Answer

Skewed to the right

Question 3

Which property is true for a normal distribution?

Accepted Answer

The mean, median, and mode are equal.

Answer

The distribution is discrete.

Answer

The curve is flat at the center.

Answer

All values are positive.

Question 4

If the mean lifespan of a bulb remains constant but the standard deviation decreases, what happens to the probability of a bulb lasting between 750 and 850 hours?

Accepted Answer

The probability increases as the standard deviation becomes smaller, making the data more concentrated around the mean.

Answer

The probability becomes irrelevant since the mean does not move.

Answer

The probability decreases because less variance means more bulbs fail earlier.

Answer

The probability remains unchanged because the mean has not changed.

Question 5

How does decreasing the standard deviation of a product's lifespan from 40 hours to 25 hours affect the probability of the product lasting within a specified range?

Accepted Answer

The probability increases because the distribution becomes more concentrated around the mean.

Answer

The probability decreases because the spread of the distribution widens.

Answer

The probability increases because the z-scores for the range become larger.

Answer

The probability remains the same because the mean lifespan does not change.

Question 6

Which of the following statements correctly describe the characteristics of a normal random variable?      I. It is symmetric about the mean.      II. The total area under the curve is equal to 1.      III. Most data values are concentrated near the mean.      IV. It includes only positive values.

Accepted Answer

I, II, and III only

Answer

I, II, III, and IV

Answer

II and IV only

Answer

I and IV only

Question 7

In a normal distribution, what percentage of data typically falls within one standard deviation of the mean?

Accepted Answer

Approximately 68%.

Answer

Approximately 95%.

Answer

Approximately 50%.

Answer

Approximately 75%.

Question 8

What is the term used to describe the distance of a data point from the mean in terms of standard deviations in a normal distribution?

Accepted Answer

Z-score.

Answer

T-score.

Answer

P-value.

Answer

Critical value.

Question 9

Fill in the blanks for the percentages of data within one, two, and three standard deviations from the mean in a normal distribution: ____%, ____%, ____%.

Accepted Answer

68%, 95%, 99.7%

Answer

60%, 75%, 85%

Answer

50%, 80%, 90%

Answer

75%, 90%, 95%

Question 10

Given a normal random variable X with μ=50 and σ=20,convert X=60 to its equivalent standard normal variable Z.

Accepted Answer

0.5

Question 11

Determine the Z-scores of

X = 120

,

140

, and

160

, given

\mu = 140

and

\sigma = 20

.

Answers: _________, _________, _________

Accepted Answer

-1&#44; 0&#44; 1

Answer

-1&#44; 0&#44; 2

Question 12

Acompany manufactures light bulbs with a lifespan that follows a normaldistribution. The mean lifespan of the bulbs is 800 hours, with a standarddeviation of 50 hours. The company wants to analyze the performance of theirproduct to ensure quality standards are met. Answer the following questions:

A light bulb is considered defective if its lifespan is less than 900 hours. What is the z-score for a bulb that lasts 900 hours?

Accepted Answer

2

Question 13

A company manufactures light bulbs with a lifespan that follows a normal distribution. The mean lifespan of the bulbs is 800 hours, with a standard deviation of 50 hours. The company wants to analyze the performance of their product to ensure quality standards are met. Answer the following questions:

What percentage of bulbs are expected to last longer than 850 hours?

Accepted Answer

15.87%

Question 14

A company manufactures light bulbs with a lifespan that follows a normal distribution. The mean lifespan of the bulbs is 800 hours, with a standard deviation of 50 hours. The company wants to analyze the performance of their product to ensure quality standards are met. Answer the following questions:

What percentage of bulbs are expected to last longer than 850 hours?

What is the probability that a randomly selected bulb lasts between 750 and 850 hours?

Accepted Answer

0.6826

Question 15

A set of test scores is normally distributed with a mean of 70 and a standard deviation of 10. What is the probability that a student scores above 85?

Accepted Answer

0.0668

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