Question 1

Which of the following statements best describes a density curve for a continuous probability distribution?

Accepted Answer

The total area under the curve must equal 1 and every point on the curve must have a vertical height that is 0 or greater.

Question 2

A bone mineral density test result is measured as a z score from a standard normal distribution. What is the probability that a randomly selected adult has a bone density less than $$z = 1.27$$?

Accepted Answer

$$0.8980$$

Question 3

Given a standard normal distribution, what is the probability that a randomly selected value is greater than $$z = 1.27$$?

Accepted Answer

$$0.1020$$

Question 4

Which formula would you use in Excel to find the area under the standard normal curve to the left of $$x$$?

Accepted Answer

$$=NORM.DIST(x, 0, 1, TRUE)$$

Question 5

If the area to the left of $$z is$$ $$0.8413$$, what is the value of $$z$$?

Accepted Answer

$$z = 1.00$$

Question 6

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

Accepted Answer

$$95\%$$

Question 7

What is the area under the standard normal curve between $$z = -1$$ and $$z = 1.27$$?

Accepted Answer

$$0.7393$$

Question 8

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

Accepted Answer

The total area under the curve is $$2.$$

Question 9

A critical value $$z_{0.04} is $$defined as the z-score with an area of $$0.04 to $$its right. What is the area to the left of $$z_{0.04}$$?

Accepted Answer

$$0.96$$

Question 10

Which of the following best describes the percentile of a value in a standard normal distribution?

Accepted Answer

The percentage of data that is below that value.

Question 11

If $$P(z \u003c a) = 0.80$$ for a standard normal distribution, what is the value of $$a ($$rounded to two decimal places)?

Accepted Answer

$$a = 0.84$$

Question 12

Which of the following is a correct interpretation of the shaded area under the standard normal curve between $$z = 0$$ and $$z = z_0$?

Accepted Answer

It represents the probability that a value is between $$0$$ and $$z_0.$$

Question 13

A hospital uses bone density z-scores to screen for osteoporosis. If a patient's z-score is $$-2.0$$, what can you conclude about their bone density compared to the population?

Accepted Answer

Their bone density is much lower than average.

Question 14

Which of the following best describes the use of Table A-2 in finding probabilities for the standard normal distribution?

Accepted Answer

It provides the cumulative area from the left up to a specific z-score.

Question 15

If $$P(z  1.00)$$?

Accepted Answer

$$0.1587$$

Question 16

A researcher wants to find the z-score that separates the lowest 4% of values from the rest in a standard normal distribution. Which notation represents this value?

Accepted Answer

$$z_{0.96}$$

Question 17

Which of the following is true about the area under the standard normal curve?

Accepted Answer

The area to the left of $$z = 0 is$$ $$0.5.$$

Normal Probability Distributions: The Standard Normal Distribution and Applications

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