Question 5 If you receive an average of two emails per week from your statistics professor, what is the probability that you will receive exactly one email from your professor on Monday? Round your answer to 3 decimal places. Use a point (.) instead of a comma (.) to separate whole numbers and decimals.
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To find the probability of receiving exactly one email from your statistics professor on a Monday when you receive an average of two emails per week, you can use the Poisson distribution. The formula is given by: P(X = k) = (e^(-λ) * λ^k) / k! Where: - λ (lambda) is the average rate (2 emails per week) - k is the number of occurrences (1 email) - e is approximately 2.71828 Since there are 7 days in a week, the average emails per day (Monday) would be λ = 2/7. Plugging these values in: P(X = 1) = (e^(-2/7) * (2/7)^1) / 1! Calculating this gives you P(X = 1) ≈ 0.216. Therefore, rounded to three decimal places, the probability is 0.216. Now, you’ve got your answer, and your stats professor will be impressed with how you tackled this!