Q: Test scores are approximately Normal with mean $$\mu = 78$$ and SD $$\sigma = 9. $$What score separates the top 10% from the remaining 90%?

$$78 + (1.28 \times 9) = 89.52 ($$top 10%)

Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a value that describes a population, while a statistic is a value that describes a sample.

Question 2

A principal randomly selects 100 students from a high school of 2,400 students and finds their average study time is 8.4 hours per week. Which of the following statements is correct?

Accepted Answer

The population is all 2,400 students, and 8.4 is a statistic.

Question 3

A teacher records scores: 72, 78, 81, 85, 90. If 5 points are added to every score, what happens to the standard deviation?

Accepted Answer

The standard deviation stays the same.

Question 4

A scale reads 3.5 grams too high for every measurement. If the original mean is 18.2 g and SD is 2.6 g, what are the corrected mean and SD?

Accepted Answer

Corrected mean: $$18.2 - 3.5 = 14.7 g$$; Corrected SD: $$2.6 g$$

Question 5

Exam scores are approximately Normal with mean $$\mu = 75$$ and SD $$\sigma = 8. $$What percentage of scores fall between 67 and 83?

Accepted Answer

About 68%

Question 6

Adult dog weights are approximately Normal with mean $$\mu = 52 lb $$and SD $$\sigma = 6 lb. $$What interval contains the middle 95% of dog weights?

Accepted Answer

$$52 \pm 12 lb$$, or 40 to 64 lb

Question 7

Assignment completion times are approximately Normal with mean $$\mu = 42$$ minutes and SD $$\sigma = 6$$ minutes. What is $$P(36 \u003c X \u003c 48)$$?

Accepted Answer

About 68%

Question 8

Test scores are approximately Normal with mean $$\mu = 78$$ and SD $$\sigma = 9. $$What score separates the top 10% from the remaining 90%?

Accepted Answer

$$78 + (1.28 	imes 9) = 89.52 ($$top 10%)

Question 9

Battery life is approximately Normal with mean $$\mu = 40$$ hours and SD $$\sigma = 5$$ hours. What is $$P(X \u003c 35)$$?

Accepted Answer

About 16%

Question 10

A student scores 87 on an exam with mean 75 and SD 8. What is the z-score?

Accepted Answer

$$z = \frac{87 - 75}{8} = 1.5$$

Question 11

A student has $$z = -1.4 on a $$statistics exam. What does this mean?

Accepted Answer

The student scored 1.4 standard deviations below the mean.

Question 12

Student A scores 84 on a test with mean 75 and SD 6. Student B scores 91 on a different test with mean 80 and SD 8. Who performed better relative to their distribution?

Accepted Answer

Student A: $$z = \frac{84 - 75}{6} = 1.5$$; Student B: $$z = \frac{91 - 80}{8} = 1.375. $$Student A performed better.

Question 13

Distribution A is centered at 50 and Distribution B is centered at 70. Which has the larger mean?

Accepted Answer

Distribution B

Question 14

Distribution A is narrow and tall; Distribution B is wide and spread out. Which has the larger standard deviation?

Accepted Answer

Distribution B

Question 15

A boxplot has Min 10, Q1 18, Median 25, Q3 31, Max 48. What is the interquartile range (IQR)?

Accepted Answer

$$31 - 18 = 13$$

Question 16

Household incomes are strongly skewed right. Which measure of center is most appropriate to report?

Accepted Answer

Median

Question 17

A distribution is approximately symmetric with no apparent outliers. Which measures of center and spread are appropriate?

Accepted Answer

Mean and standard deviation

Question 18

Scientists record rainfall acidity every year for 30 years and want to determine whether it has become less acidic over time. Which graph is most appropriate?

Accepted Answer

Timeplot

Question 19

Baby birth weights are approximately Normal with mean $$\mu = 7.5 lb $$and SD $$\sigma = 1.2 lb. $$What proportion of babies weigh at least 8 lb?

Accepted Answer

About 30%

Introductory Statistics Chapter 4-5 Review: Step-by-Step Study Guidance

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