Assume that the height of a type of tree has a normal probability distribution with a mean of 85.9 ft and a standard deviation of 9.4 ft. A tree of this type grows in my backyard and it stands 59.6 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. My neighbor also has a tree of this type growing in her backyard, but hers stands 74.6 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers. Enter your answers as decimals accurate to 3 decimal places.

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Assume that the height of a type of tree has a normal probability distribution with a
mean of 85.9 ft and a standard deviation of 9.4 ft.
A tree of this type grows in my backyard and it stands 59.6 feet tall. Find the
probability that the height of a randomly selected tree is as tall as mine or shorter.
My neighbor also has a tree of this type growing in her backyard, but hers stands 74.6
feet tall. Find the probability that the full height of a randomly selected tree is at
least as tall as hers.
Enter your answers as decimals accurate to 3 decimal places.
Transcribed Image Text:Assume that the height of a type of tree has a normal probability distribution with a mean of 85.9 ft and a standard deviation of 9.4 ft. A tree of this type grows in my backyard and it stands 59.6 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter. My neighbor also has a tree of this type growing in her backyard, but hers stands 74.6 feet tall. Find the probability that the full height of a randomly selected tree is at least as tall as hers. Enter your answers as decimals accurate to 3 decimal places.
Expert Solution
Step 1

Let us denote X= height of a tree

Given that X follows a normal distribution with mean=85.9 and standard deviation= 9.4

 

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