Question
In: Statistics and Probability
Tree heights: Cherry trees in a certain orchard have heights that are normally distributed with mean...
Tree heights: Cherry trees in a certain orchard have heights that are normally distributed with mean =μ108 inches and standard deviation =σ13. (a) What proportion of trees are more than 131 inches tall? (b) What proportion of trees are less than 102 inches tall? (c) What is the probability that a randomly chosen tree is between 98 and 100 inches tall? Round the answers to four decimal places
Solutions
Expert Solution
Let "X" be the height of the tree.
Note: P(Z>a)=1-P(Z<a)
Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(1.7692, TRUE)" to find the probability.
The proportion of trees are more than 131 inches tall is
.------------------------------------------------------------------------------------------------
Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(0.4615, TRUE)" to find the probability.
The proportion of trees are less than 102 inches tall is
.------------------------------------------------------------------------------------------------
Note: P(a<Z<b)=P(Z<b)-P(Z<a)
Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(-0.6154, TRUE)" & "=NORM.S.DIST(-0.7692, TRUE)" to find the probability.
The probability that a randomly chosen tree is between
98 and 100 inches tall is 
orchestra answered 2 years agoRelated Solutions
Cherry trees in a certain orchard have heights that are normally distributed with mean = μ...
Cherry trees in a certain orchard have heights that are normally
distributed with mean = μ 106 inches and standard deviation = σ 17
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