Let the random variable X follow a normal distribution with µ = 0.2 and σ^2 = 0.0025. a. Find the probability that X is greater than 0.4. b. Find the probability that X is greater than 0.15 and less than 0.28. c. Find the probability that X is less than 0.10. d. What is the number such that the probability is 0.2 that X is greater than that number? e. What are the two numbers between which the probability is 0.05 that X is in the symmetric interval about the mean?
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4, we first need to find the z-score for 0.4. The z-score is calculated as: z = (X - µ) / σ where µ is the mean and σ is the standard deviation. In this case, µ = 0.2 and σ = sqrt(0.0025) = 0.05. So, the z-score for 0.4 is: z = (0.4 - 0.2) / 0.05 = 4 Now, we Show more…
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