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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 the standard deviation of the distribution is 2.5 pounds. Find the probability that the mean of a sample of 32 families will be between 16.4 and 17.4 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final answer to four decimal places and intermediate z-value calculations to two decimal places.

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Expert Solution

Solution :

Given that,

mean = = 17.2

standard deviation = = 2.5

n = 32

= = 17.2

= / n = 2.5 / 32 = 0.442

P(16.4 < < 17.4)  

= P[(16.4 - 17.2) / 0.442 < ( - ) / < (17.4 - 17.2) / 0.442 )]

= P(-1.81 < Z < 0.45)

= P(Z < 0.45) - P(Z < -1.81 )

Using z table,  

= 0.6736 - 0.0351

= 0.6385

orchestra answered 1 year ago
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