Question

Find the mean and standard deviation for each binomial random variable:

a. n = 46, π = .60 (Round your mean value to 2 decimal places and standard deviation to 4 decimal places.)

Mean
Standard deviation

b. n = 84, π = .40 (Round your mean value to 2 decimal places and standard deviation to 4 decimal places.)

Mean
Standard deviation

c. n = 35, π = .85 (Round your mean value to 2 decimal places and standard deviation to 4 decimal places.)

Mean
Standard deviation

Answer 1

(A) we know that the formula for the mean is given as mean = n*p

And standar deviation formula is given as

SD= sqrt(n*p*(1-p)).............here sqrt means square root

where n is the sample size and p is the probability

setting the given value of n and p

Mean = 46*0.60 = 27.60

SD = sqrt(46*0.6(1-0.6))= sqrt(46*0.6*0.4)= sqrt(11.04) = 3.3226

(B) we know that the formula for the mean is given as mean = n*p

And standar deviation formula is given as

SD= sqrt(n*p*(1-p)).............here sqrt means square root

where n is the sample size and p is the probability

setting the given value of n and p

Mean = 84*0.4 = 33.60

SD = sqrt(84*0.4(1-0.4))= sqrt(84*0.4*0.6)= sqrt(20.16) = 4.4900

(C) we know that the formula for the mean is given as mean = n*p

And standar deviation formula is given as

SD= sqrt(n*p*(1-p)).............here sqrt means square root

where n is the sample size and p is the probability

setting the given value of n and p

Mean = 35*0.85 = 29.75

SD = sqrt(35*0.85(1-0.85))= sqrt(46*0.85*0.15)= sqrt(4.4625) = 2.1125