The turkey found in a particulaar country have an average weight of 15.6 lbs. Wi

Question

The turkey found in a particulaar country have an average weight of 15.6 lbs. With a standard deviation of 4.0 pounds. Forty-five turkeys are randomly selected for a county fair.

A. Find the probability that the average weight of the turkey will be less than 14.5 lbs.

B. What is the probability that the average weight of the turkey will be more than 17 lbs?

C. Find the probability that the average weight of the turkey will be between 15 and 16 pounds.

Please show the work for all of these questions.

Thanks

Explanation / Answer

Mean = 15.6

Sd = 4

n = 45

A) P(X bar < 14.5) = P(Z < (14.5 - 15.6) / (4/sqrt(45))

= P(Z < - 1.84)

= 0.0329

B) P(X bar > 17) = P(Z > (17 - 15.6)/(4/sqrt (45))

= P(Z > 2.35)

= 1 - P(Z < 2.35)

= 1 - 0.9906

= 0.0094

C) P(15 < X bar < 16) = P((15 - 15.6)/(4/sqrt(45)) < Z < (16 - 15.6)/(4/sqrt(45))

= P(-1.01 < Z < 0.67)

= P(Z < 0.67) - P(Z < - 1.01)

= 0.7486 - 0.1562

= 0.5924

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