Q: Given the probabilities from the previous question, are speeding and alcohol independent?

No, because $$0.10 \neq 0.40 \times 0.25$$

Question 1

Given the summary statistics for repair bills: Min = $$27$$, Q1 = $$88$$, Median = $$132$$, Q3 = $$308$$, Max = $$1442$$, Mean = $$284$$, SD = $$140$$, determine if there are any outliers using the IQR method. Which of the following is correct?

Accepted Answer

There is at least one outlier because the maximum value is greater than $$Q3 + 1.5 	imes IQR$$

Question 2

A service manager estimates your repair bill will be $$90. Based on the summary statistics (Q1 = 88$, Median = 132$, Mean = 284$), is this bill unusually low?

Accepted Answer

Yes, because $$90 is $$below Q1 and much lower than the mean

Question 3

If your US salary is $$750 ($$median), and in China salaries are converted by $$Salary_{China} = 8 	imes Salary_{US} + 200$$, what is the median salary in China?

Accepted Answer

$$6400$$

Question 4

If your US salary has a z-score of $$+1.20$$, what will your z-score be after converting to Chinese salary using $$Salary_{China} = 8 	imes Salary_{US} + 200$$?

Accepted Answer

It will remain $$+1.20$$

Question 5

Given the regression model $$Price = 15,327 - 0.11 	imes Miles$$ with $$r^2 = 0.47$, what does the slope represent?

Accepted Answer

For each additional mile, the price decreases by $$0.11$$

Question 6

A Subaru with 42,000 miles is for sale. Using the model $$Price = 15,327 - 0.11 	imes Miles$$, what is the predicted price?

Accepted Answer

$$10,707$$

Question 7

Doctors inject penicillin and measure concentration over time. The data suggest an exponential decay. Which transformation would best linearize the data?

Accepted Answer

Plotting log(concentration) vs. time

Question 8

A forester models tree diameter vs. age and then re-expresses the model using $$\log(Age). $$The $$R^2$$ increases from 70% to 84.3%. What does this suggest?

Accepted Answer

The log model fits the data better

Question 9

Using the regression $$Diam = -8.6077 + 15.0701 	imes \log(Age)$$, what is the predicted diameter for a 50-year-old tree? (Use $$\log_{10}(50) \approx 1.699)$$

Accepted Answer

$$17.98$$

Question 10

Police reports: 40% of accidents involved speeding, 25% involved alcohol, and 10% involved both. What is the probability an accident involved neither?

Accepted Answer

$$0.45$$

Question 11

Given the probabilities from the previous question, are speeding and alcohol independent?

Accepted Answer

No, because $$0.10 
eq 0.40 	imes 0.25$$

Question 12

SAT prep: 5% took prep, 30% of them admitted to first choice, 20% of others admitted. If a student was admitted, what is the probability they did NOT take prep?

Accepted Answer

$$0.93$$

Question 13

Bowling: Men's mean = $$154$$, SD = $$9$$; Women's mean = $$144$$, SD = $$12. $$What is the expected mean difference (Man - Woman)?

Accepted Answer

$$10$$

Question 14

Using the bowling data, what is the standard deviation of the difference in scores (assuming independence)?

Accepted Answer

$$\sqrt{9^2$ + 12^2$}$$

Question 15

State officials claim 18% of adults smoke. What is the expected number of people you must ask to find a smoker?

Accepted Answer

$$1/0.18$$

Question 16

Let $$X be $$the number of smokers in a sample of 30 adults. What is the probability model for $$X$$?

Accepted Answer

Binomial$$(n=30, p=0.18)$$

Question 17

For the strange dice: Die A has faces 1, 3, 3, 3, 3, 3; Die B has faces 2, 2, 2, 2, 6, 6. What is the mean total when rolling both dice?

Accepted Answer

$$7$$

Question 18

If you want to maximize your chance of rolling a higher number than your opponent, which die should you choose?

Accepted Answer

Die B, because it has a higher chance of rolling a 6

Unit 2 Exam Review – Step-by-Step Statistics Guidance

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드