Q: If two events $$A$$ and $$B$$ are independent, which of the following is true?

$$P(A \cap B) = P(A) \times P(B)$$

Question 1

A researcher used the regression equation $$	ext{ExamScore} = 50.263 + 3.427 	imes 	ext{HoursStudied} to $$predict exam scores. What is the predicted exam score for a student who studied for 8 hours?

Accepted Answer

$$77.679$$

Question 2

A computer program randomly generates a digit from 0 to 9. What is the sample space for this experiment, and how many possible outcomes are there?

Accepted Answer

Sample space: $$\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$; Number of possible outcomes: $$10$$

Question 3

A hospital has 3,200 nurses and 1,800 doctors. Of the nurses, 480 have completed advanced training, while 720 doctors have completed advanced training. Are the events "being a nurse" and "having completed advanced training" independent?

Accepted Answer

No

Question 4

In a manufacturing process, the probability that an item is defective is $$0.15. $$For a quality check involving four randomly selected items, what is the probability that all four items are non-defective?

Accepted Answer

$$0.474$$

Question 5

A cafe analyzed whether customers tipped based on their payment method. What is the probability that a customer did not tip, given that the customer paid by card?

Accepted Answer

$$0.60$$

Question 6

If the probability that an event $$E$$ will not occur is $$P(\overline{E}) = 0.86$$, what is the probability that the event will occur?

Accepted Answer

$$0.14$$

Question 7

A survey of 800 college students found that 280 admitted to speeding regularly, 190 admitted to using their phones while biking, and 60 admitted to doing both. What is the probability that a randomly selected student either sped regularly or used a phone while biking, but not both?

Accepted Answer

$$0.5347$$

Question 8

If the probability of event $$A is$$ $$0.2$$ and the probability of event $$B is$$ $$0.3$$, what is the probability of either event $$A or $$event $$B$$ occurring if they are mutually exclusive?

Accepted Answer

$$0.5$$

Question 9

A consumer feedback agency surveyed 1,115 shoppers about a new store policy. According to the Pareto chart, what is the probability of selecting a shopper who believes the policy is extremely unfair?

Accepted Answer

$$0.39$$

Question 10

Suppose the probability that a randomly selected manufactured item is defective is $$p = 0.15. $$What is the probability that, in a sample of four items, at least one is defective?

Accepted Answer

$$1 - (0.85)^4$

Question 11

Given the regression output, what is the 95% confidence interval for the mean exam score for students who studied 8 hours?

Accepted Answer

$$(75.020, 80.338)$$

Question 12

Based on the tipping data, what is the probability that a randomly selected customer left a tip?

Accepted Answer

$$\frac{33 + 18}{110}$$

Question 13

If two events $$A$$ and $$B$$ are independent, which of the following is true?

Accepted Answer

$$P(A \cap B) = P(A) 	imes P(B)$$

Question 14

A student claims that the probability of either event $$A or $$event $$B$$ occurring is $$P(A) + P(B) - P(A \cap B). $$Under what condition does this formula simplify to $$P(A) + P(B)$$?

Accepted Answer

When $$A$$ and $$B$$ are mutually exclusive

Question 15

If the probability that a customer pays by card is $$0.545$$ and the probability that a customer did not tip given they paid by card is $$0.60$$, what is the probability that a randomly selected customer both paid by card and did not tip?

Accepted Answer

$$0.545 	imes 0.60$$

Probability and Statistics Study Guidance – Ch. 3

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드