(a) Let X be the number of times you swim in a given week when you have visited the gym on 4 occasions. What kind of distribution does X follow? Interpret the parameters of this distribution. (b) What assumptions do you need to make to say that X has this distribution? (c) What is the probability that you swim every time you visit the ARC in a given week? (d) What is the probability that you swim in the pool at least 3 times in a given week? (e) What is the probability that you use the pool less than twice during a given week? Round your answer to 3 decimal places.

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Counting And Probability
Section9.3: Binomial Probability
Problem 2E: If a binomial experiment has probability p success, then the probability of failure is...
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You go to the ARC gym 4 times a week, each time you visit there is a 0.85 probability that you will
swim in the pool. You make this choice independently of other times you have visited the gym the same
week.
We will now consider how many times you use the pool in a given week.
(a) Let X be the number of times you swim in a given week when you have visited the gym on 4
occasions. What kind of distribution does X follow? Interpret the parameters of this distribution.
(b) What assumptions do you need to make to say that X has this distribution?
(c) What is the probability that you swim every time you visit the ARC in a given week?
(d) What is the probability that you swim in the pool at least 3 times in a given week?
(e) What is the probability that you use the pool less than twice during a given week? Round your
answer to 3 decimal places.
Transcribed Image Text:You go to the ARC gym 4 times a week, each time you visit there is a 0.85 probability that you will swim in the pool. You make this choice independently of other times you have visited the gym the same week. We will now consider how many times you use the pool in a given week. (a) Let X be the number of times you swim in a given week when you have visited the gym on 4 occasions. What kind of distribution does X follow? Interpret the parameters of this distribution. (b) What assumptions do you need to make to say that X has this distribution? (c) What is the probability that you swim every time you visit the ARC in a given week? (d) What is the probability that you swim in the pool at least 3 times in a given week? (e) What is the probability that you use the pool less than twice during a given week? Round your answer to 3 decimal places.
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