1. Power companies severely trim trees growing near their lines to avoid power failures due to fallinglimbs in storms. Applying a chemical to slow the growth of the trees is cheaper than trimming, but thechemical kills some of the trees. Suppose that one such chemical would kill 20% of sycamore trees.The power company tests the chemical on 250 sycamores. Consider this a SRS from the populationof all sycamore trees. Calculate the probability that less than 24% of the tress in the sample arekilled. (Hint: Shape, Center, Spread, Curve, Calculations, Conclusion....)

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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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1. Power companies severely trim trees growing near their lines to avoid power failures due to falling
limbs in storms. Applying a chemical to slow the growth of the trees is cheaper than trimming, but the
chemical kills some of the trees. Suppose that one such chemical would kill 20% of sycamore trees.
The power company tests the chemical on 250 sycamores. Consider this a SRS from the population
of all sycamore trees. Calculate the probability that less than 24% of the tress in the sample are
killed. (Hint: Shape, Center, Spread, Curve, Calculations, Conclusion....)

Expert Solution

Step 1

Given Information:

Sample size (n) = 250

Proportion = 20% = 0.20

To calculate the probability that less than 24% of the trees in the sample are killed:

Mean $μ_{\hat{p}} = 0.20$

Standard deviation of sample proportion is calculated as follows:

$\begin{array}{rcl} σ_{\hat{p}} & = & \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}} \\ = & \sqrt{\frac{0.20 (1 - 0.20)}{250}} \\ = & \sqrt{\frac{0.16}{250}} \\ = & 0.02529822128 \\ \approx & 0.0253 \end{array}$

Z-score is a measure which tells how many standard deviations away, a data value is, from the mean. It is given by the formula:

$z = \frac{X - μ}{σ}$

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