Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 10.8 years, and standard deviation of 2.7 years.

If you randomly purchase one item, what is the probability it will last longer than 8 years? (Give answer to 4 decimal places.)

Answer 1

µ =    10.8                          
σ =    2.7                          
right tailed                              
P ( X ≥   8.00   )                      
                              
Z =   (X - µ ) / σ = (   8.00   -   10.8   ) /    2.7   =   -1.037
                              
P(X ≥   8   ) = P(Z ≥   -1.037   ) =   P ( Z <   1.037   ) =    0.8501(answer)

excel formula for probability from z score is =NORMSDIST(Z)