Question

?34% of women consider themselves fans of professional baseball. You randomly select four women and ask each if she considers herself a fan of professional baseball. Complete parts? (a) and? (b) below.??

(a) Construct a binomial distribution using? n=4 and? p=.34. ? (Hint: Find? P(x) for? x=0, 1,? 2, 3, 4. Refer to section? 4.2)

?????

?(b) Find the mean and standard deviation of the binomial distribution.

Answer 1

Formula for binomial distribution is P(x) = C(n,x)*(p^x)*(1-p)^(n-x)

we have p =0.34, 1-p = 1-0.34 = 0.66, n = 4

(A)

Binomial distribution

for x = 0, we get  P(0) = C(4,0)*(0.34^0)*(1-0.34)^(4-0) = 4!/[(4-0)!*0!]*0.34^0*0.66^4 = 0.1897

for x = 1, we get  P(1) = C(4,1)*(0.34^1)*(1-0.34)^(4-1) = 4!/[(4-1)!*1!]*0.34^1*0.66^3 = 0.3910

for x = 2, we get  P(2) = C(4,2)*(0.34^2)*(1-0.34)^(4-2) = 4!/[(4-2)!*2!]*0.34^2*0.66^2 = 0.3021

for x = 3, we get  P(3) = C(4,3)*(0.34^3)*(1-0.34)^(4-3) = 4!/[(4-3)!*3!]*0.34^3*0.66^1 = 0.1038

for x = 4, we get  P(4) = C(4,4)*(0.34^4)*(1-0.34)^(4-4) = 4!/[(4-4)!*4!]*0.34^4*0.66^0 = 0.0134

So, Binomial distribution is

X	P(X)
0	0.1897
1	0.3910
2	0.3021
3	0.1038
4	0.0134

(B) we have n = 4 and p = 0.34

Mean = n*p

setting the given values, we get

4*0.34 = 1.36

so, mean = 1.36

Standard deviation =

setting the given values, we get

standard deviation = = 0.9474