Suppose among all the 50 faculty members of School of Arts & Science, 30 of them

Question

Suppose among all the 50 faculty members of School of Arts & Science, 30 of them support Democrat, 17 support Republican and 3 support other parties. Now 10 faculty members will be randomly selected from the fifty to participate in a round-table meeting. What is the probability that exactly 5 pro-Democrat faculty members will be selected? What is the probability that no selected faculty member supports other parties. What is the probability that more than 15 pro-Republican faculty members will be selected? Let X = the number of selected pro-Democrat faculty members. Find the expected value and the standard deviation of X.

Explanation / Answer

Given info is,
among 50 faculty members of school of arts and science
democrat= 30; p(democrat) = 30/50 = 0.6
republican=17; P(republican) = 17/50 = 0.34
other parties = 3; P( other parties) = 3/50 = 0.06
& now 10 faculty members will be randomly selected from the fifty
a.
P(democrat) = P( X = 5 ) = ( 10 5 ) * ( 0.6^5) * ( 1 - 0.6 )^5
= 0.2007
b.
P( X = 0 ) = ( 10 0 ) * ( 0.06^0) * ( 1 - 0.06 )^10
= 0.5386
c.
insuffcient info as value of n is unknown,though in question it is given
n=10, but the required probability here to find is for 15
d.
Mean ( np ) =10 * 0.6 = 6
Standard Deviation ( npq )= 10*0.6*0.4 = 1.5492
Normal Distribution = Z= X- u / sd                   

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