Question

Use the binomial expression (p+q)^n to calculate abinomial distribution with n = 5 and p = 0.3.

Answer 1

The binomial distributions are :

0.16807

0.36015

0.3087

0.1323

0.02835

0.00243

EXPLANATION :

In a binomial distribution of (p + q)^n :

n = 5

p = 0.3 and

q = 1 - p = 1 - 0.3 = 0.7

`_nC_x(p)^x(q)^(n-x)`

We are going to get the values from x = 0 to 5

`\begin{gathered} _5C_0(0.3)^5(0.7)^(5-0)=0.16807 \\ _5C_1(0.3)^5(0.7)^(5-1)=0.36015 \\ _5C_2(0.3)^5(0.7)^(5-2)=0.3087 \\ _5C_3(0.3)^5(0.7)^(5-3)=0.1323 \\ _5C_4(0.3)^5(0.7)^(5-4)=0.02835 \\ _5C_5(0.3)^5(0.7)^(5-5)=0.00243 \end{gathered}`