For each of the following uncertain quantities, discuss whether it is reasonable to assume that the...

For each of the following uncertain quantities, discuss whether it is reasonable to assume that the probability distribution of the quantity is binomial. If you think it is, what are the parameters n and p? If you think it isn’t, explain your reasoning.

a. The number of wins the Boston Red Sox baseball team has next year in its 81 home games

b. The number of free throws Kobe Bryant misses in his next 250 attempts

c. The number of free throws it takes Kobe Bryant to achieve 100 successes

d. The number out of 1000 randomly selected customers in a supermarket who have a bill of at least $150

e. The number of trading days in a typical year where Microsoft’s stock price increases

f. The number of spades you get in a 13-card hand from a well-shuffled 52-card deck

g. The number of adjacent 15-minute segments during a typical Friday where at least 10 customers enter a McDonald’s restaurant

h. The number of pages in a 500-page book with at least one misprint on the page.

Solutions

Expert Solution

a. The number of wins the Biston Red Sox baseball team has next year is a binomial random variable. Here, n is the number of games i.e. 81 and p is the probability of winning each game.

b. The number or free throws Kobe Bryant misses in his next 250 attempts is a Binomial random variable. Here, n = 250, p = the probability of missing a free throw.

c. The number of free throws it takes Kobe Bryant to achieve 100 successes is not a binomial random variable as the number of trials are not fixed in this case.

d. The number of customers out of 1000 will be a Binomial random variable with probability of success is the probability of having a bill greater than or equal to $150 and n = 1000.

e. Assuming there are no cases when the stock price will remain same, the number of trading days in a typical year when Microsoft's stock price increases will be a Binomial random variable. Here, n = 365, p = the probability that the stock price will increase.

f. The number of spades in a 13 card hand is a Binomial random variable with n = 13, p = 13/52 = 0.25 [Since, there are 13 spades in a hand of 52 cards].

g. Here, the variable is not a Binomial random variable as the total number of trials is not fixed.

h. The number of pages with at least one misprint on the page is a Binomial random variable. Here, n = 500, p = the probability of at leat one misprint.

orchestra answered 1 year ago

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