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# Binomial Probability Distribution and Probability

1. Suppose that the number of cars, X, that pass through a car wash between 4:00pm and 5:00pm on any sunny Friday has the following probability distribution:

X 4 5 6 7 8 9
P(X=x) 1/12 1/12 ¼ ¼ 1/6 1/6

What is the probability that at least 7 cars pass through the car wash?

2. A large university that is better known for its football program than its academic strength claims that 80% of its football players graduate. An investigation examines the fate of all 20 players who enter the program over a period of several years that ended 6 years ago. Of these players, 11 graduated and 9 are no longer in school. If the university's claim is true, the number of players who graduate among the 20 studied should have the Binomial (20, 0.8) distribution.

a. Determine the mean number of graduates out of 20 players assuming the university's claim is true.
b. Find the probability that 11 or fewer player's graduate.
c. What can you conclude?

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1. Suppose that the number of cars, X, that pass through a car wash between 4:00pm and 5:00pm on any sunny Friday has the following probability distribution:

X 4 5 6 7 8 9
P(X=x) 1/12 1/12 ¼ ¼ 1/6 1/6

What is the probability that at least 7 cars pass through the car wash?