Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 14 years, and standard deviation of 2.6 years. If you randomly purchase one item, what is the probability it will last longer than 8 years?

Answer 1

Given that ,

mean = = 14

standard deviation = = 2.6

n = 1

= 14

= / n =2.6 / 1 = 2.6

P( >8 ) = 1 - P( <8 )

= 1 - P[( - ) / < (8 -14) /2.6 ]

= 1 - P(z <-2.31 )

Using z table

= 1 - 0.0104

= 0.9896

probability= 0.9896