Question 1

Which of the following variables is a discrete random variable?

Accepted Answer

The number of pieces of candy in a bag

Question 2

Which of the following is NOT a requirement for a binomial experiment?

Accepted Answer

The probability of success changes from trial to trial

Question 3

Given the following probability distribution for a random variable X:

x: 0, 1, 2, 3
P(x): 0.1, 0.3, 0.4, 0.2

What is the mean $$\mu of X$$?

$$\mu = \sum x \cdot P(x)$$

Accepted Answer

$$\mu = 1.7$$

Question 4

A random variable X has the following probability distribution:

x: -1, 1, 2, 3
P(x): 0.5, 0.3, 0.15, 0.05

What is the expected value $$E(X)$$?

Accepted Answer

$$E(X) = 0.2$$

Question 5

Which of the following scenarios describes a continuous random variable?

Accepted Answer

The amount of milk in a randomly selected gallon jug

Question 6

Suppose a binomial experiment has $$n = 10$$ trials and probability of success $$p = 0.3. $$What is the probability of exactly 4 successes?

$$P(X = 4) = {10 \choose 4} (0.3)^4$ (0.7)^6$

Accepted Answer

$$P(X = 4) = 0.2001$$

Question 7

A casino game pays $$3 if you win, 2 if $$you tie, and $0 if you lose. The probabilities are 0.1, 0.2, and 0.7, respectively. What is the expected payout?

Accepted Answer

$$E(X) = 0.7$$

Question 8

Which of the following best describes the mean of a discrete random variable?

Accepted Answer

The long-run average value of the random variable

Question 9

If $$X is a $$binomial random variable with $$n = 20$$ and $$p = 0.4$$, what is the standard deviation $$\sigma$$?

$$\sigma = \sqrt{np(1-p)}$$

Accepted Answer

$$\sigma = 2.19$$

Question 10

A real estate investor buys a property for $$50,000 and spends 27$$,000 on repairs. They can sell it for $$120,000 (probability 0.15), 100$$,000 (0.45), $$80,000 (0.25), or 60$$,000 (0.15). What is the expected profit?

Accepted Answer

$$E(X) = 19$$,500$

Question 11

Which of the following statements about the binomial probability distribution is TRUE?

Accepted Answer

The mean is given by $$\mu = np$$

Question 12

Suppose $$X is a $$discrete random variable with mean $$\mu = 2$$ and standard deviation $$\sigma = 1.5. If $$you repeat the experiment 1000 times, what value will the sample mean $$\bar{x}$$ approach?

Accepted Answer

$$\bar{x}$$ will approach 2

Question 13

A binomial experiment is performed with $$n = 8$$ and $$p = 0.6. $$What is the probability of at least 6 successes?

$$P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8)$$

Accepted Answer

$$P(X \geq 6) = 0.296$$

Question 14

Which phrase from the table corresponds to the mathematical symbol $$\leq$$?

Accepted Answer

"no more than" or "at most" or "less than or equal to"

Question 15

If a binomial experiment has $$n = 50$$ and $$p = 0.2$$, what is the shape of the probability distribution as $$n$$ increases?

Accepted Answer

It becomes approximately bell-shaped

Question 16

A student claims that in a binomial experiment, the probability of success must be different for each trial. Is this claim correct?

Accepted Answer

No, the probability of success must be the same for each trial

Chapter 6 STATS

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