Module 4 Quiz

Quiz Instructions

Answer all 15 multiple-choice questions
You need 11 out of 15 (70%) correct to pass
You'll receive immediate feedback with explanations
You can retake the quiz as many times as needed

Question 1

According to the Empirical Rule, approximately what percent of data falls within ONE standard deviation of the mean in a normal distribution?

a) 50%

b) 68%

c) 95%

d) 99.7%

Question 2

Scores on a test are normally distributed with μ = 80 and σ = 5. What range contains approximately 95% of all scores?

a) 70 to 90

b) 75 to 85

c) 65 to 95

d) 60 to 100

Question 3

Which statement is TRUE about a normal distribution?

a) The mean is always greater than the median

b) The distribution is skewed to the right

c) The mean, median, and mode are all equal

d) About 50% of data falls within 1 standard deviation

Question 4

Calculate the z-score for x = 130 when μ = 100 and σ = 15.

a) z = 1.5

b) z = 2.0

c) z = 2.5

d) z = 3.0

Question 5

A data value has a z-score of −1.8. What does this tell you?

a) The value is 1.8 units above the mean

b) The value is 1.8 standard deviations below the mean

c) The value is unusually high

d) The value equals the mean

Question 6

For a normal distribution with μ = 50 and σ = 8, find x when z = 2.5.

a) x = 58

b) x = 62

c) x = 66

d) x = 70

Question 7

For a standard normal distribution, P(Z < 1.0) ≈ 0.8413. What is P(Z > 1.0)?

a) 0.1587

b) 0.5000

c) 0.8413

d) 0.9200

Question 8

Given P(Z < 1.5) = 0.9332 and P(Z < 0.5) = 0.6915, find P(0.5 < Z < 1.5).

a) 0.2417

b) 0.3085

c) 0.6247

d) 1.6247

Question 9

Heights are normally distributed with μ = 68 inches and σ = 4 inches. What is the first step to find P(X < 72)?

a) Look up 72 in the z-table

b) Calculate z = (72 − 68) / 4

c) Divide 72 by 68

d) Multiply 68 by 4

Question 10

Test scores are normally distributed with μ = 75 and σ = 10. A score of 95 has z = 2.0. Using the z-table where P(Z < 2.0) = 0.9772, what percent of students scored ABOVE 95?

a) 2.28%

b) 50%

c) 97.72%

d) Cannot determine

Question 11

The z-score for the 84th percentile is approximately:

a) z = 0.5

b) z = 1.0

c) z = 1.5

d) z = 2.0

Question 12

SAT scores are normally distributed with μ = 1000 and σ = 200. If the z-score for the 75th percentile is 0.67, what SAT score represents the 75th percentile?

a) 1067

b) 1100

c) 1134

d) 1200

Question 13

To be in the top 5% of a normal distribution, you need a z-score of approximately:

a) z = 1.28

b) z = 1.65

c) z = 1.96

d) z = 2.33

Question 14

A manufacturing process produces parts with mean length 10.0 cm and standard deviation 0.5 cm (normally distributed). Parts shorter than 9.0 cm or longer than 11.0 cm are defective. What percent are defective?

a) About 2.5%

b) About 5%

c) About 10%

d) About 32%

Question 15

Anna scored 85 on Test 1 (μ = 75, σ = 5) and 78 on Test 2 (μ = 70, σ = 4). On which test did she perform better relative to her class?

a) Test 1

b) Test 2

c) Equal performance on both

d) Cannot determine without knowing class size

Quiz Instructions

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