Question

A survey found that Americans generate an average of 16 pounds of glass garbage each year. Assume the standard deviation of the distribution is 3.4 pounds. Find the probability that the mean of a sample of 64 families will be between 14.6 and 17.8 pounds.

Answer 1

Solution :

Given that ,

mean = = 16

standard deviation = = 3.4

n = 64

= 16

=  / n= 3.4 / 64=0.425

P(14.6<     < 17.8) = P[(14.6-16) /0.425  < ( - ) /   < (17.8-16) /0.425 )]

= P( -3.29< Z < 4.24)

= P(Z < 4.24) - P(Z < -3.29)

Using z table

=1-0.0005

=0.9995

probability= 0.9995