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Question

According to the Federal Communications Commission , 70% of all us households have vcrs. In a random sample of 15 households, what is the probability that less than 8 have vcrs?

Answer 1

Binomial p=0.7, N-15, 0 <=k <=7

Sum [ (15 choose k) 0.7 ^k 0.3^(15-k) ], k=0,1,2,3,4,5,6,7

Normal approx. to binomial:

mean = Np = 15*0.7 = 10.5

stdDev = sqrt(npq) = sqrt( 15 * 0.7 * 0.3) =

Prob ( -0.5 <= x < 7.5) =

> 5% just over 5%