Question

Hey , i am lost on how to solve it. All i know is that it is hypergeometric distribuition.

5. A lab contains 10 computers which were chosen at random from a supply of 26 computers, 18 of which were Dells. Let X represents the number of Dell computers in this lab. [5+5+10 = 20 points] (a) What is the distribution of X? Give the name and corresponding parameters (b) Calculate the mean value and the standard deviation of X (c) What is the probability that there are exactly 4 Dell computers in this lab?

Answer 1

a) distribution is hypergeometric with parameter ; total size N=26 ; sample size n=10 and target population k=18

b)

mean E(X)=nk/N =10*18/26=6.9231

std deviation =sqrt(nk/N*(1-k/N)*(N-n)/(N-1))=sqrt(10*18/26*(1-18/26)*(26-10)/(26-1))=1.1676

c)

P(X=4)=¹⁸C₄*⁸C₆ /²⁶C₁₀ =0.016130