Question 1

Which of the following best describes the meaning of the z-score in the context of the normal distribution?

Accepted Answer

It measures how many standard deviations a value is from the mean.

Question 2

Given an area of $$0.93 to $$the left under the standard normal curve, what is the corresponding z-score?

Accepted Answer

$$z = 1.48$$

Question 3

If you are asked to find the z-score that separates the top $$7\%$$ from the rest of the population, what is the first step?

Accepted Answer

Subtract $$0.07$$ from $$1 to $$get $$0.93$$ and then find the z-score for $$0.93$$ area to the left.

Question 4

What is the correct interpretation of the notation $$z_{\alpha}$$?

Accepted Answer

It is the z-score with an area of $$\alpha to $$its right.

Question 5

If you are given the 88th percentile ($$P_{88}$$), how do you find the corresponding z-score using the z-table?

Accepted Answer

Find the area $$0.88 in $$the table, locate the two closest values, and average their z-scores.

Question 6

A medical test result is considered unusual if it falls in the lowest $$5\% of $$the distribution. What z-score would separate these unusual results from the rest?

Accepted Answer

$$z = -1.64$$

Question 7

Which calculator function is used to find the z-score corresponding to a given area under the normal curve?

Accepted Answer

invNorm

Question 8

If you want to find the z-score that separates the highest $$4\% of a $$distribution from the rest, which area should you use with InvNorm?

Accepted Answer

$$0.96$$

Question 9

A university wants to award scholarships to students in the top $$10\% of $$SAT scores. What z-score should they use as the cutoff?

Accepted Answer

$$z = 1.28$$

Question 10

If you use InvNorm($$0.04) on $$your calculator, what z-score do you get and how should you interpret it?

Accepted Answer

$$z = -1.75$$, which is the z-score with $$0.04$$ area to its left

Question 11

Why is it important to use a diagram when solving normal distribution area problems?

Accepted Answer

It helps visualize the area and clarify which side of the mean is being considered.

Question 12

A pharmaceutical company wants to identify the bottom $$93\% of $$patients based on a biomarker. Which z-score should they use as the cutoff?

Accepted Answer

$$z = 1.48$$

Question 13

If you are given an area to the right (such as $$\alpha = 0.10$$), how do you find the corresponding z-score using the z-table?

Accepted Answer

Subtract $$\alpha$$ from $$1$$ and look up the resulting area to the left in the table.

Question 14

If the z-table gives two areas equally close to the desired area, what should you do?

Accepted Answer

Average the two corresponding z-scores.

Question 15

A researcher wants to find the z-score that separates the lowest $$4\% of a $$distribution. What is the correct z-score?

Accepted Answer

$$z = -1.75$$

Question 16

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

Accepted Answer

The area to the left of $$z = 0 is $$always $$0.50.$$

Question 17

If you use InvNorm($$0.90) on $$your calculator, what z-score do you get?

Accepted Answer

$$z = 1.28$$

Question 18

A company wants to identify employees in the top $$4\% of $$performance scores. Which z-score should they use as the cutoff?

Accepted Answer

$$z = 1.75$$

Question 19

Which of the following is the correct process for finding the z-score corresponding to a given percentile?

Accepted Answer

Find the area in the z-table closest to the percentile, then use the corresponding z-score.

Reverse Lookup of z-Scores and Critical Values in the Normal Distribution

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