63% of men consider themselves professional baseball fans. You randomly select 1

Question

63% of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is (a) exactly eight, (b) at least eight, and (c) less than eight If convenient, use technology to find the probabilities. (a) P(8) = _____ (Round to the nearest thousandth as needed.) (b) P(x Greaterthanorequalto 8) = _____ (Round to the nearest thousandth as needed) (c) P(x

Explanation / Answer

Solution:

We are given n = 10 and p = 63% = 0.63

We have to use binomial distribution for finding the required probabilities.

Formula for binomial probability is given as below:

P(X=x) = nCx*p^x*q^(n x)

Where, q = 1 – p = 1 – 0.63 = 0.37

Part a

Here, we have to find P(X=8)

P(X=8) = 10C8*0.63^8*0.37^(10 – 8)

P(X=8) = 0.152876

Required probability = 0.153

Part b

Here, we have to find P(X8)

P(X8) = 1 – P(X<8)

P(X8) = 1 – P(X7)

P(X7) = 0.779429

(By using Excel command =binomdist(7,10,0.63,1))

P(X8) = 1 – 0.779429

P(X8) = 0.220571

Required probability = 0.221

Part c

Here, we have to find P(X<8)

P(X<8) = P(X7)

(By using Excel command =binomdist(7,10,0.63,1))

P(X<8) = 0.779429

Required probability = 0.779

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