Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.6 years,
and standard deviation of 0.7 years. If you randomly purchase one item, what is the probability it will
last longer than 4 years?

Answer 1

Answer:  

=3.6 , =0.7, n=1

P(x > 4) =?

Z = 0.571429

Z=0.57

P(x > 4) = 1 - P(Z 0.57)

now, look to normal z table to get  P(Z 0.57)

we get,

P(Z 0.57) = 0.7157

now, P(x > 4) = 1 - P(Z 0.57)

P(x > 4) = 1- 0.7157

P(x > 4) = 0.2843

probability of item will last longer than 4 years =  0.2843