Question

The weight of an adult swan is normally distributed with a mean of 26 pounds and a standard deviation of 7.2 pounds. A farmer randomly selected 36 swans and loaded them into his truck. What is the probability that this flock of swans weighs > 1000 pounds?

Answer 1

If the flock of 36 swans weighed 1000 pounds, the mean weight would be 1000/36 = 27.78 pounds.
The standard deviation of the sample is given by:
\[\large \sigma _{\bar{W}}=\frac{7.2}{\sqrt{36}}=1.2\]
Let the mean weight of the sample be W-bar.
\[\large P(\bar{W}>27.78)=P(Z >\frac{27.78-26}{1.2})=P(Z >1.48)\]
Reference to a standard normal distribution table gives the required probability as 0.069.