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Question

A manufacturer knows that their items have a normally distributed lifespan with a mean of 2.5 years and a standard deviation of 0.5 years the 5% of items with the shortest lifespan will last less than how many years give your answer in one decimal place

Answer 1

mean = 2.5 years, standard deviation = 1/2 year

the 5% of the items with shortest lifespan will last less than how many years?

lowest 5% means CI = mean +/- 90% which means a z score of 1.645

CI = mean +/- zs = 2.5 +/- 1.645(.5) = 2.5+/-.8225

= (1.6775, 3.3225)

round to one decimal place (1.7, 3.3)