5. (a) Given that X is normally distributed with mean 10 and P(X > 12) = 0.1587. What is the probability that X will fall in the interval (9, 11)? You are given; (1) = 0.8413 and +(-;)= 0.3085, where (z) = P(-∞ < Z < z)such that Z~N(0,1). %3D

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5. (a) Given that X is normally distributed with mean 10 and P(X > 12) =
0.1587. What is the probability that X will fall in the interval (9, 11)? You
are given; Þ(1) = 0.8413 and
*(-;)-
= 0.3085, where P(z) =
P(-∞ < Z < z)such that Z~N(0,1).
(b) Suppose that during rainy season on a tropical island the length of the
shower has an exponential distribution, with parameter 1 = 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?
Transcribed Image Text:5. (a) Given that X is normally distributed with mean 10 and P(X > 12) = 0.1587. What is the probability that X will fall in the interval (9, 11)? You are given; Þ(1) = 0.8413 and *(-;)- = 0.3085, where P(z) = P(-∞ < Z < z)such that Z~N(0,1). (b) Suppose that during rainy season on a tropical island the length of the shower has an exponential distribution, with parameter 1 = 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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