Assume that X is normally distributed with a mean of 6 and a standard deviation of 3. Determine the value for x that solves for each of the following.
(a) P(X>x) = 0.95
(b) P(x<X<9) = 0.2
(c) P(3<X<x) = 0.8
The tensile strength of paper is modeled by a normal distribution with a mean of 35 pounds per square inch and a standard deviation of 2 pounds per square inch.
(a) What is the probability that the strength of a sample is less than 39 lb/in^2
(b) If the specifications require the tensile strength to exceed 29 lb/in^2 , what proportion of the sample is scrapped?
Suppose that X represents time measurements from a gamma distribution with a mean of 4 minutes and a variance of 2 minutes^2.
(a) Find the parameters λ and r.
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