Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 8.1 years, and standard deviation of 2.2 years.

If you randomly purchase 4 items, what is the probability that their mean life will be longer than 11 years? (Give answer to 4 decimal places.)

Answer 1

Solution :

Given that ,

mean = =8.1

standard deviation = = 2.2

n = 4

= 8.1

= / n = 2.2/ 4 = 11

P( >11 ) = 1 - P( <11 )

= 1 - P[( - ) / < (11-8.1) /1.1 ]

= 1 - P(z <2.64 )

Using z table

= 1 - 0.9959

= 0.0041