Question

The average beer consumption in America is 4.5 liters per year, with a standard deviation of 3.5 liters.

a. What is the probability that a random sample of 75 Americans produces a mean beer consumption between 4 and 6 liters per year?

Please show the hand calculations.

Answer 1

Solution:

Given that,

= 4.5

= 3.5

n = 75

So,

= 4.5

=  ( /n) = ( 3.5 / 75 ) = 0.4041

a ) p ( 4 <   < 6 )

= p( 4 - 4.5 / 0.4041 ) ( -  / ) < ( 6 - 4.5 / 0.4041)

= p ( - 0.5 / 0.4041 < z < 1.5 / 0.4041 )

= p ( - 1.24 < z < 3.71)

= p (z < 3.71 ) - p ( z < - 1.24 )

Using z table

= 0.9999 - 0.1075

= 0.8924

Probability = 0.8924