can you explain how to standardize this? ste
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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can you explain how to standardize this? step by step by explaining pls
Transcribed Image Text:A gardener buys a large batch of young spruce trees and will plant these trees in his tree
nursery. It is known that the length of the young spruce trees is normally distributed with a
mean of 25 cm and that only 5% of the young spruce trees are shorter than 20 cm.
a)
Determine the probability that a random tree from this batch has a length that lies
between 22 and 30 cm.
b)
The gardener always takes 40 trees from this batch at random and plants them in his
nursery in one row. Determine the probability that in such a row of trees, there are at
least two trees shorter than 20 cm.
After some years, when the trees have been able to grow well, the gardener decides to cut
the spruce trees and to sell them during the Christmas season. We can assume that the length
of the spruce trees for sale is still normally distributed with a mean of 180 cm and a variance
of 484 cm². The trees are divided into two price categories: small trees of 40 euro each and
large trees of 55 euro each. The gardener wants the expected revenue per tree to be 48 euro.
c) Set up the probability distribution for the revenue of one spruce tree.
d) What is the greatest length for a spruce tree to be classified as 'small'?
Answer question 4
Z.
X-25
~N (0₂1)
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Step 1: Given Information:
VIEWStep 2: Use standard normal distribution and the information about the mean and percentage.
VIEWStep 3: a. The probability that a random tree from this batch has a length that lies between 22 and 30 cm.
VIEWStep 4: b. The probability that in such a row of trees, there are at least two trees shorter than 20 cm.
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