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The heights of a certain type of tree are approximately normally distributed with a mean height p = 5 ft and a standard

deviation o = 0.4 it. Which statement must be true?​

User Sgwill
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2 Answers

5 votes

Answer:

D. A tree with a height of 6.2 ft is 3 standard deviations above the mean

Explanation:

User Rohan Bhatia
by
8.1k points
5 votes

Answer:

A tree with a height of 6.2 ft is 3 standard deviations above the mean

Explanation:


1^s^t statement: A tree with a height of 5.4 ft is 1 standard deviation below the mean(FALSE)

an X value is found Z standard deviations from the mean mu if:


(X-\mu)/(\sigma) = Z

In this case we have:
\mu=5\ ft
\sigma=0.4\ ft

We have four different values of X and we must calculate the Z-score for each

For X =5.4\ ft


Z=(X-\mu)/(\sigma)\\Z=(5.4-5)/(0.4)=1

Therefore, A tree with a height of 5.4 ft is 1 standard deviation above the mean.


2^n^d statement:A tree with a height of 4.6 ft is 1 standard deviation above the mean. (FALSE)

For X =4.6 ft


Z=(X-\mu)/(\sigma)\\Z=(4.6-5)/(0.4)=-1

Therefore, a tree with a height of 4.6 ft is 1 standard deviation below the mean .


3^r^d statement:A tree with a height of 5.8 ft is 2.5 standard deviations above the mean (FALSE)

For X =5.8 ft


Z=(X-\mu)/(\sigma)\\Z=(5.8-5)/(0.4)=2

Therefore, a tree with a height of 5.8 ft is 2 standard deviation above the mean.


4^t^h statement:A tree with a height of 6.2 ft is 3 standard deviations above the mean. (TRUE)

For X =6.2\ ft


Z=(X-\mu)/(\sigma)\\Z=(6.2-5)/(0.4)=3

Therefore, a tree with a height of 6.2 ft is 3 standard deviations above the mean.

User Uchenna Nwanyanwu
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8.6k points

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