20 A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.1 years, andstandard deviation of 1.6 years.The 3% of items with the shortest lifespan will last less than how many years?Give your answer to one decimal place.

Name: 20 A manufacturer knows that their items have a normally distributed l
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 20 A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.1 years, andstandard deviation of 1.6 years.The 3% of items with the shortest lifespan will last less than how many years?Give your answer to one decimal

Given:- X~normal distribution meanμ=11.1 yearsstandard deviationσ=1.6 year and PX≥x = 0.03 We have to calculate xnow, PX≥x = 0.03PX<x = 1-0.03PX<x = 0.97 now, z = x-μσ =0.97 x-11.11.6=0.97x = 0.97×1.6+11.1x = 12.652 Answer is 12.652