Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 7.8 years, and standard deviation of 2.5 years. If you randomly purchase 15 items, what is the probability that their mean life will be longer than 7 years?

Answer 1

The probability of mean lifespan of items will be longer than 7 years is 0.8925

Solution - Let y be the life span of items. Lifespan standard deviation 2 = 2.5 years. It can be is normally distributed coith mean H = 4.8 years, and written symbolically as Xi NN (M = 7.8, 32= (2-5)2) A sample size of n=15 items be purchased randomly from normal population. Therefore we can say that X-M NN (011) Blin Z = X -7.8 NN (0, 1) > (1) 2.5/115 The probability that their mean life.will be longer than 7 years is given as X-H T-M p(x+y)= 9 3/ja 8|ip X-7.8 7-7.8 2.5/J15 2.5W15 = P(2>-1:24) where Z=X -7.8 R-5/15 (Due to symmetry). : P(Z < 1:24) = 1-P (271-24) ..P(777) 1-0 1075 p(*>7) = 0.8925