Approximately 90% of freshmen at Marquette University receive financial aid.21 Suppose 20 Marquette freshmen are randomly selected.
a. Find the probability that at most 15 freshmen receive financial aid.
b. Find the probability that at least 12 freshmen receive financial aid.
c. Find the expected number of freshmen who receive financial aid.
d. Suppose at least 15 freshmen receive financial aid. What is the probability that all 20 freshmen receive financial aid?
The battery manufacturer Varta sells a car battery with 800 coldcranking amps and advertises great performance even in bitingly cold weather. Varta claims that after sitting on a frozen Minnesota lake for 10 days at temperatures below 32°F, this battery will still have enough power to start a car. Suppose the actual probability of starting a car following this experiment is 0.75, and 15 randomly selected cars (equipped with this battery) are subjected to these grueling conditions.
a. Find the probability that fewer than 10 cars will start. Write a Solution Trail for this problem.
b. Find the probability that more than 12 cars will start.
c. Suppose 9 cars actually start. Is there any evidence to suggest that the probability of starting a car is different from 0.75? Justify your answer.
Levain Bakery, on West 74th Street in New York City, is trying to determine the number of loaves of raisin bread to make each day. Over the past few months the store has baked 50 loaves each day and has sold out with probability 0.80. Suppose the owner continues this practice and 30 days are selected at random.
a. What is the expected number of days on which all 50 loaves will be sold?
b. Find the probability of selling all 50 loaves on at least 20 days.
c. Find the probability of selling all 50 loaves on at most 18 days.