(a) Given that X is normally distributed with mean 10 and ?(? > 12) = 0.1587. What is the probability that X will fall in the interval (9, 11)? You are given:  Φ(1) = 0.8413 and Φ(−1/2)=0.3085, where Φ(?) = ?(−∞ < ? < ?)such that ?~?(0,1). (b) Suppose that during rainy season on a tropical island the length of the shower has an exponential distribution, with parameter ? = 2, time being measured in minutes. What is the probability that a shower will last more than three minutes? If a shower has already lasted for 2 minutes, what is the probability that it will last for at least one more minute?

A First Course in Probability (10th Edition)
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(a) Given that X is normally distributed with mean 10 and ?(? > 12) = 0.1587. What is the probability that X will fall in the interval (9, 11)? You are given:  Φ(1) = 0.8413 and Φ(−1/2)=0.3085, where Φ(?) = ?(−∞ < ? < ?)such that ?~?(0,1).

(b) Suppose that during rainy season on a tropical island the length of the shower has an exponential distribution, with parameter ? = 2, time being measured in minutes. What is the probability that a shower will last more than three minutes? If a shower has already lasted for 2 minutes, what is the probability that it will last for at least one more minute?

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