Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.8 years, and standard deviation of 1.2 years. If you randomly purchase 22 items, what is the probability that their mean life will be longer than 12 years?

Answer 1

Solution :

Given that ,

mean = = 11.8

standard deviation = =1.2

n = 22

=  11.8

= / n = 1.2 / 22 = 0.2558

P( > 12) = 1 - P( <12 )

= 1 - P[( - ) / < (12 -11.8) / 0.2558]

= 1 - P(z <0.78)

Using z table

= 1 - 0.7823

= 0.2177

probability= 0.2177