Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.7 years, and standard deviation of 0.7 years.

If 6 items are picked at random, 4% of the time their mean life will be less than how many years?

Give your answer to one decimal place.

Answer 1

µ=   2.7                  
σ = 0.7/ sqrt(6) = 0.285773803                  
proportion=   0.04                  
                      
Z value at    0.04   =   -1.75   (excel formula =NORMSINV(   0.04   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   -1.75   *   0.285773803   +   2.7  
X   =   2.20   (answer)          

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