You must be logged in to reply to this topic.
- E2P3
Viewing 7 posts - 1 through 7 (of 7 total)
You must be logged in to reply to this topic.
You must be logged in to reply to this topic.
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.
You must be logged in to reply to this topic.
Ursula C. Schwerin Library
New York City College of Technology, C.U.N.Y
300 Jay Street, Library Building - 4th Floor
Our goal is to make the OpenLab accessible for all users.