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In: Statistics and Probability

A survey found that the American family generates an average of 17.2 pounds of glass garbage...

A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume population is normally distributed with standard deviation of 2.5 pounds. Find the probability that the mean of a sample of 55 families will generate between 17 and 18 pounds.

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Expert Solution

Solution :

Given that ,

mean =   = 17.2

standard deviation = = 2.5

n = 55

= 17.2

=  / n= 2.5 / 55=0.34

P(17<     <18 ) = P[(17-17.2) / 0.34< ( - ) /   < (18-17.2) /0.34 )]

= P(-0.59 < Z < 2.35)

= P(Z< 2.35 ) - P(Z <-0.59 )

Using z table

=0.9906 - 0.2776

=0.7130

probability= 0.7130

orchestra answered 2 years ago
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