Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3 years, and standard deviation of 0.6 years.

If you randomly purchase 17 items, what is the probability that their mean life will be longer than 3 years?

Answer 1

Solution :

Given that,

mean = = 3

standard deviation = =0.6

n=17

= =3

= / n =0.6 / 17 = 0.1455

P( > 3) = 1 - P( < 3)

= 1 - P[( - ) / < (3-3) /0.1455 ]

= 1 - P(z <0 )

Using z table

= 1 - 0.5

= 0.5

probability= 0.5