The production time, in minutes, of a manufacturing item is a continuous random variable X with density function

for some suitable constants b and c.
(i) If it is known that E(X) = 13∕9, what are the values of b and c?
(ii) Calculate the standard deviation of X.
(iii) Find the probability that, among the next three items which will be produced, none will have a production time of less than one minute.

Transcribed Image Text:

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