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The federal government has found that 70% of environmental complaints are valid. The government received 119,000 complaints last year. Let be random variable which is 1 if ith complaint is valid and 0 otherwise. Let X be the random variable which counts the number of valid complaints last year.
a) Find expectation for and X and interpret.
b) Find standard deviation for and X and interpret.
E[X] = n*p = mean = 119,000 * 0.70 = 83,300 out of the 119,000 are valid complaints. standard deviation = sqrt(n*p*q). q=1-P = 1-.7 = 0.3 so std= sqrt(83,000 * 0.3) = 158.0822. One standard deviation from the mean is 158.0822 units. This question is easy to preceive, but I am a little confused about the interpretation of the standard deviation.
I agree with the way you solved this problem due to the example provided in the book. However, you forgot to put the variance which is Var[X]=np(1-p), this gives you 83,300 (1-0.70) which gives you 24,990….and the square root of that is yes 158.08…but your input of your square root is wrong…it should be std=sqrt(83,300*0.30)=158.08. =)
By the way you only interpret the expectation and standard deviation for X. Your forgot to do it for Xi. Expectation-E[Xi]= p =0.70 and Variance-Var[Xi]=p(1-p)=0.70(1-0.70)=0.21. Therefore, the Square root of the answer for the variance will give you the answer for your standard deviation for Xi, which is Sqrt(0.21)=.458
Correct solution, all steps shown! -_- I’m dead tired.
what about Xi?
Sorry didn’t label correctly. First one is Xi. All solutions are there.
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