Probability MC Practice - Chapter 6

A marketing survey compiled data on the number of personal computers in households. If X = the number of computers in a randomly-selected household, and we omit the rare cases of more than 5 computers, then X has the following distribution. What is the probability that a randomly chosen household has at least two personal computers?

• (a) 0.19

• (b) 0.20

• (c) 0.29

• (d) 0.39

• (e) 0.61

A random variable X has a probability distribution as follows. Where k is a positive constant. The probability P(X < 2.0) is equal to

• (a) 0.90.

• (b) 0.25.

• (c) 0.65.

• (d) 0.15.

• (e) 1.00.

A business evaluates a proposed venture as follows. It stands to make a profit of $10,000 with probability 3/20, to make a profit of $5000 with probability 9/20, to break even with probability 5/20, and to lose $5000 with probability 3/20. The expected profit in dollars is

• (a) 1500.

• (b) 0.

• (c) 3000.

• (d) 3250.

• (e) –1500.

Roll one 8-sided die 10 times. The probability of getting exactly 3 sevens in those 10 rolls is given by

• 50.3%

• 9.6%

• 0%

• 11.95%

• 9.2%

X and Y are independent random variables, and a and b are constants. Which one of the following statements is true?

• 
• 
• 
• 
• 

Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is Normal with mean $360 and standard deviation $50. What is P(X > $400)?

• 0.2119

• 0.2881

• 0.5319

• 0.7881

• 0.8450

A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards. Let Y be the number of red cards (hearts or diamonds) in the 40 cards selected. Which of the following best describes this setting?

• Y has a binomial distribution with n = 40 observations and probability of success p = 0.5.

• Y has a binomial distribution with n = 40 observations and probability of success p = 0.5, provided the deck is shuffled well.

• Y has a binomial distribution with n = 40 observations and probability of success p = 0.5, provided that after selecting a card it is replaced in the deck and the deck is shuffled well before the next card is selected.

• Y has a geometric distribution with n = 40 observations and probability of success p = 0.5.

• Y has a geometric distribution with n = 52 observations and probability of success p = 0.5.

Which of the following is a true statement?

• The binomial setting requires that there are only two possible outcomes for each trial, while the geometric setting permits more than two outcomes.

• A geometric random variable takes on integer values from 0 to n.

• If X is a geometric random variable and the probability of success is 0.85, then the probability distribution of X will be skewed left, since 0.85 is closer to 1 than to 0.

• An important difference between binomial and geometric random variables is that there is a fixed number of trials in a binomial setting, and the number of trials varies in a geometric setting.

• The distribution of every binomial random variable is skewed right.