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The heights of pecan trees are normally distributed with a mean of 10 feet

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The heights of pecan trees are normally distributed with a mean of 10 feet and a standard deviation of 2 feet.
1. Show work.

(a) What is the probability that a randomly selected pecan tree is between 9 and 12 feet tall? (Round the answer to 4 decimal places)

(b) Find the 75th percentile of the pecan tree height distribution. (Round the answer to 2 decimal places)

2. Show work.

(a) For a sample of 64 pecan trees, state the standard deviation of the sample mean (the “standard error of the mean”). (Round your answer to three decimal places)

(b) Suppose a sample of 64 pecan trees is taken. Find the probability that the sample mean heights is between 9.5 and 10 feet. (Round your answer to four decimal places)

 
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