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[answered] Let X represent the number of days per week that your stati


Let X represent the number of days per week that your statistics professor goes to the gym. Assume that the number of days your professor goes to the gym during one week is independent of the number of days he goes during each other week.

x ? P(X = x)
1 ? 0.10
2 ?0.35
3 ?0.55

(a) Consider a sample of two weeks. What is the sampling distribution of the average number of days per week that your professor goes to the gym during those two weeks? That is, what is the sampling distribution of X based on n = 2? (HINT: Set up a probability table forX.)

(b) Consider an entire year (i.e. 52 weeks). What is the approximate sampling distribution of X? Include the values of any relevant parameters.

(c) Approximate the probability that over the course of an entire year, your professor goes to the gym an average of at least 2.3 days per week.

 


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