Question

A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.8 years, and standard deviation of 1.1 years. If you randomly purchase 21 items, what is the probability that their mean life will be longer than 4 years? (Give answer to 4 decimal places.)

Answer 1

Solution :

Given that ,

mean = = 3.8

standard deviation = = 1.1

n = 21

= 3.8

= / n = 1.1 / 21 = 0.24

P( > 4) = 1 - P( < 4)

= 1 - P[( - ) / < (4-3.8) /0.24 ]

= 1 - P(z <0.83 )

Using z table

= 1 - 0.7967

= 0.2033

probability= 0.2033