Answer:
a) Hyper-geometric distribution
b1) P(X=2) = 0.424
b2) P(X>2) = 0.152
C1) Mean of X = 1.67
C2) Standard Deviation of X = 0.65
Step-by-step explanation:
b1) P(X = 2) = (5C2 * 7C2)/(12C4) = (10 * 21)/(495) = 210/495
P(X=2) = 0.424
b2) P(X>2) = 1 - P(X≤2) = 1 - [P(X=0) + P(X=1) + P(X=2)]
P(X=0) = (7C4)/(12C4) = 35/495 = 0.071
P(X=1) = (5C1 * 7C3)/(12C4) = (5 * 35)/(495) = 175/495 = 0.354
P(X=2) = 0.424
P(X>2) = 1 - P(X≤2) = 1 - [0.424 + 0.071 + 0.354]
P(X>2) = 0.152
C1) Mean of X = nk/N
k = number of 3-megapixel cameras = 5
n = number of selected cameras = 4
N = Total number of cameras = 12
Mean of X = 5*4/12
Mean of X = 1.67
C2) Standard Deviation of X
Standard deviation of X=(nk/N*(1-k/N)*(N-n)/(N-1))1/2
Standard Deviation of X=(4*(5/20)*(1-5/12)*((12-4)/(12-1))^1/2 =0.65
Standard Deviation of X = 0.65
