According to the CICA Business Monitor, 11% of Canada’s executive chartered accountants are pessimistic about the economy.26 To check this claim, 50 chartered accountants were randomly selected and asked whether they feel pessimistic about the economy in 2013.
a. If the claim is true, find the probability that exactly seven chartered accountants are pessimistic about the economy.
b. If the claim is true, find the probability that at most four chartered accountants are pessimistic about the economy.
c. Suppose 12 chartered accountants are pessimistic about the economy. Is there any evidence to suggest that the claim is false? Justify your answer.
In the movie Lethal Weapon, the character played by Joe Pesci is concerned about drive-thru windows at fast-food restaurants. Suppose the probability that an order at a drive-thru window at a fast-food restaurant will be filled correctly is 0.75. Twenty orders are selected at random.
a. What is the probability that exactly 15 orders will be filled correctly?
b. What is the probability that at most 12 orders will be filled correctly?
c. What is the probability that between 10 and 14 (inclusive) orders will be filled correctly?
d. Suppose two groups of 20 random orders are independently selected. What is the probability that at least 16 orders will be filled correctly in both groups?
The reality television series Splash! features celebrities attempting to learn how to dive. The first episode aired in January 2013 and earned a 23.6% audience share. That is, 23.6% of all TVs in use during the show time period were tuned to a station airing Splash!. 27 Twenty people who watched TV during that time period were selected at random.
a. Find the probability that at least six watched Splash!.
b. Find the expected number of people who watched Splash!. Find the probability that the number of people who watched Splash! is less than the mean.
c. Suppose that at most four people watched Splash!. What is the probability that no one watched Splash!?