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(20 points) The length of life of an instrument produced by a machine has a normal distribution with a mean of 15 months and standard

(20 points) The length of life of an instrument produced by a machine has a normal distribution with a mean of 15 months and standard deviation of 3 months. Let X be the length of life of an instrument produced by that machine.

a) Find the probability that an instrument produced by this machine will lastless than 11 months. (5 points)

c) Find the probability that an instrument produced by this machine will lastbetween 12 and 13 months. (5 points)

d) Complete the following statement: probability that an instrument produced by this machine will last more than _______ months is 0.35. (5 points)

e) Suppose that 25 instruments produced by this machine were randomly selected and the length of their life was recorded. Find the probability that the mean length of life for the sample of 25 instruments is greater than 16 months. List any assumptions that you had to make. (5 points)

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