Bank overdraft fees range from $10 to $38, consumers believe they are annoying and excessive, and these fees are a huge revenue source for banks.42 The Overdraft Protection Act of 2013 is designed to limit overdraft fees in a variety of ways and to require fees to be reasonable and proportional to the amount of the overdraft. Let X be the amount of an overdraft fee for a randomly selected bank. The probability distribution for X is given in the table below.
a. Find the mean, variance, and standard deviation of the overdraft amount.
b. Find the probability that a randomly selected bank has an overdraft fee greater than $25.
c. Find the probability that a randomly selected bank has an overdraft fee less than m 2 s.
d. Suppose three banks are selected at random. What is the probability that at least one bank has an overdraft fee less than $20?
Thales Alenia Space is a European company that manufactures communications satellites. Researchers at the company have determined that the most common reason for a satellite to fail once it is in orbit is a problem related to opening and initiating the solar panels. Suppose the probability of a failure related to the solar panels is 0.08.
a. What is the probability that the fifth satellite launched will be the first to fail due to a solar-panel problem?
b. What is the expected number of satellites launched until the first one fails due to a solar-panel problem?
c. Thales Alenia Space is preparing an advertising campaign in which they claim to have had 20 successful launches in a row. What is the probability that the first failure due to a solar-panel problem will occur after the 20th launch?