Q: Given the same $$P(A)$$, $$P(B)$$, and $$P(A \cap B) as $$above, are events $$A$$ and $$B$$ independent?

No, because $$P(A \cap B) \neq P(A) \times P(B)$$

Q: Two cards are drawn at random from a standard deck of 52 cards. What is the probability that both are aces?

$$\frac{4}{52} \times \frac{3}{51}$$

Q: In Pet World, 25% of people are Cat People. In a random sample of 500, what is the standard error of the sample proportion?

$$\sqrt{\frac{0.25 \times 0.75}{500}}$$

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

Given the following probability distribution for a discrete random variable $$X$$:

$$x$$: 0, 1, 2, 3, 4, 5

$$P(x)$$: 0.05, 0.3, ?, 0.2, 0.1, 0.05

What is the value of $$P(2)$$?

Accepted Answer

$$0.25$$

Question 2

Suppose 88% of customers would buy another PC from Micron. If four customers are selected at random, what is the probability that all four would purchase another Micron PC? (Round to four decimal places)

Accepted Answer

$$0.5997$$

Question 3

Given $$P(A) = 0.2$$, $$P(B) = 0.6$$, and $$P(A \cap B) = 0.15$$, what is $$P(A \cup B)$$?

Accepted Answer

$$0.65$$

Question 4

Given the same $$P(A)$$, $$P(B)$$, and $$P(A \cap B) as $$above, are events $$A$$ and $$B$$ independent?

Accepted Answer

No, because $$P(A \cap B) 
eq P(A) 	imes P(B)$$

Question 5

A fair die is rolled. Let $$A = \{1,2,3,4\}$$ and $$B = \{3,4,6\}. $$What is $$P(A \cap B)$$?

Accepted Answer

$$\frac{2}{6}$$

Question 6

For the same events $$A$$ and $$B$$ above, what is $$P(A|B)$$?

Accepted Answer

$$\frac{2}{3}$$

Question 7

Are the events $$A = \{1,2,3,4\}$$ and $$B = \{3,4,6\}$$ mutually exclusive?

Accepted Answer

No, because $$A$$ and $$B$$ share elements $$3$$ and $$4$$

Question 8

Two cards are drawn at random from a standard deck of 52 cards. What is the probability that both are aces?

Accepted Answer

$$\frac{4}{52} 	imes \frac{3}{51}$$

Question 9

The lifetime of an electrical part is normally distributed with mean $$100$$ hours and standard deviation $$20$$ hours. What is the probability that a part lasts less than $$104$$ hours?

Accepted Answer

$$P(Z \u003c 0.2)$$

Question 10

Suppose 60% of all Honda vehicles sold in North America are made there. If 15 Hondas are randomly selected, what is the probability that exactly 10 were made in North America? (Let $$X be $$the number made in North America.)

Accepted Answer

$$\binom{15}{10} (0.6$$)^{10}$$ (0.4)^5$

Question 11

A random sample of 985 likely voters found 592 intend to vote for the GOP candidate. What is the point estimate for the proportion of likely voters who intend to vote for the GOP candidate?

Accepted Answer

$$\frac{592}{985}$$

Question 12

Assume human body temperatures are normally distributed with mean $$98.2^\circF $$and standard deviation $$0.62^\circF. $$What $$z-$$score corresponds to a temperature of $$100.6^\circF$$?

Accepted Answer

$$z = \frac{100.6 - 98.2}{0.62}$$

Question 13

In Pet World, 25% of people are Cat People. In a random sample of 500, what is the standard error of the sample proportion?

Accepted Answer

$$\sqrt{\frac{0.25 	imes 0.75}{500}}$$

Question 14

Which of the following best defines mutually exclusive events?

Accepted Answer

Events that cannot occur at the same time

Question 15

What is the expected value $$E(X) of a $$discrete random variable $$X$$ with possible values $$x_i$$ and probabilities $$p_i$$?

Accepted Answer

$$E(X) = \sum x_i p_i$$

Question 16

Which of the following is a property of a continuous probability distribution?

Accepted Answer

The probability that the random variable takes any exact value is zero

Question 17

What is the margin of error for a confidence interval for a population proportion $$p$$ with sample proportion $$\hat{p}$$, sample size $$n$$, and critical value $$z^*$$?

Accepted Answer

$$z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$

Question 18

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 19

A confidence level of 95% means:

Accepted Answer

If we repeated the sampling process many times, about 95% of the confidence intervals would contain the true parameter

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

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