Statistics Help with finding sample standard deviation, please?

Question

I'm given this problem:
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"Power companies 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 the sycamore trees. The power company tests this chemical on 250 sycamores. Consider these as an SRS from the population of all sycamore trees.

(a) What are the mean and standard deviation of the number of trees in the sample that are killed?
(b) What is the probability that at least 60 trees (24% of the sample) are killed?"
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I found the mean (20% of 250 = 50), but I have no clue on how to find the sample standard deviation here..

Can someone help me out with how to get it in this case? No other information was given. No data set, no population standard deviation. Everything in that problem is everything I have to use.

Polygon · Accepted Answer

This is a binomial problem

p = 20% or  0.20
q = (1 - p) = 0.80
n = 250
mean = np = 250*0.20 = 50
Variance = npq = 250*0.20*0.80 = 40
Standard Deviation = sqrt(variance) = sqrt(40) = 6.32

Mohd_Nawi · Answer

(a) Standard question. Binomial, mean=np=250*0.20=50, variance=np(1-p)=40, standard dev=sqrt(40).
(b) P{X>60}=P{Z>z}, z=(60-50)/sqrt(40) = 1.58
p=P{Z<-1.58}=0.0571.

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Statistics Help with finding sample standard deviation, please?

3 Answers