Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 11.4 years, and standard deviation of 2 years. If you randomly purchase 12 items, what is the probability that their mean life will be longer than 12 years?

Answer 1

Solution :

Given that ,

mean = = 11.4

standard deviation = = 2

n = 12

= 11.4

= / n = 2/ 12= 0.5774

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

= 1 - P[( - ) / < (12 -11.4) / 0.5774]

= 1 - P(z <1.04 )

Using z table

= 1 - 0.8508

= 0.1492

probability= 0.1492