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36 % of women consider themselves fans of professional baseball. You randomly select six women and ask each if she considers herself a fan of professional baseball. Complete parts​ (a) through​ (c) below.
​(a) Construct a binomial distribution using
n equals 6n=6 and
p=0.36.



x
​P(x)
0

nothing
1

nothing
2

nothing
3

nothing
4

nothing
5

nothing
6

nothing
​(Round to the nearest thousandth as

Answer :

nobillionaireNobley
The probability of a binomial distribution with n trials is given by
[tex]P(x)=^nC_x\cdot p^{n-x}\cdot q^x[/tex]
where, p is the probability of success and q = (1 - p) is the probability of failure.

Given n = 6 and p = 0.36, then q = 1 - 0.36 = 0.64

For x = 0,
[tex]P(x)=P(0)=^6C_0(0.36)^6(0.64)^0=0.002[/tex]

For x = 1,
[tex]P(x)=P(1)=^6C_1(0.36)^5(0.64)^1=6(0.00605)(0.64)=0.023[/tex]

For x = 2,
[tex]P(x)=P(2)=^6C_2(0.36)^4(0.64)^2=15(0.01680)(0.4096)=0.103[/tex]

For x = 3,
[tex]P(x)=P(3)=^6C_3(0.36)^3(0.64)^3=20(0.046656)(0.262144)=0.245[/tex]

For x = 4,
[tex]P(x)=P(4)=^6C_4(0.36)^2(0.64)^4=15(0.1296)(0.167772)=0.326[/tex]

For x = 5,
[tex]P(x)=P(5)=^6C_5(0.36)^1(0.64)^5=6(0.36)(0.107374)=0.232[/tex]

For x = 6,
[tex]P(x)=P(6)=^6C_6(0.36)^0(0.64)^6=0.069[/tex]

Therefore, the binomial distribution table is as follows:
[tex]\begin{center} \begin{tabular} {|c|c|c|c|c|c|c|c|} x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ [1ex] P(x) & 0.002 & 0.023 & 0.103 & 0.245 & 0.326 & 0.232 & 0.069 \end{tabular} \end{center}[/tex]

Notice that the sum of the P(x) row is 1.

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