Assume a binomial probability distribution with n=40 and =0.26. Compute the foll

Question

Assume a binomial probability distribution with n=40 and =0.26. Compute the following: (Round all z values to 2 decimal places.)

a. The mean and standard deviation of the random variable. (Round your "" to 4 decimal places and mean to 1 decimal place.) =10.4 = 2.7742

b. The probability that X is 15 or more. (Use the rounded values found above. Round your answer to 4 decimal places.) Probability

c. The probability that X is 5 or less. (Use the rounded values found above. Round your answer to 4 decimal places.) Probability

Explanation / Answer

given n= 40 and p= =0.26

1)

mean = = np=40*0.26= 10.4

The variance of the binomial distribution is

V(X) = 2 = npq = 40*0.26*(1-0.26) = 7.696

standard deviation () =  7.696 1/2 = 2.7742

P( Xb 15 ) =

40
P(Xb = x)
x = 25

P( Xn 15 )
= P( Z ( 15-10.4 ) / 2.7742 )
= P( Z 1.685 )
= 0.0465

P(Xb 5 ) =

5
P(Xb = x)
x = 0

P( Xn < 5 )
= P( Z < ( 5 - 10.4 ) / 2.7742 )
= P( Z <-1.9465 )
= 0.0256 ( use Z table)

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