Question

A) Find the binomial probability P(x = 5), where n = 12 and p = 0.70.
(B) Set up, without solving, the binomial probability P(x is at most 5) using probability notation.
(C) How would you find the normal approximation to the binomial probability P(x = 5) in part A? Please show how you would calculate µ and σ in the formula for the normal approximation to the binomial, and show the final formula you would use without going through all the calculations.

Answer 1

A.) P(x = 5) = C(12,5)(.3^5)(.7^7) = .158
b.) P(x<=5) = P(x=0) + P(x=1)+...+P(x=5).
So, P(x=i) = C(12,i)(.3^i)(.7^(12-i))

C.) Use µ = .3(12)= 3.6, σ = sqrt(12(.3)(.7)) = 1.5874
If N is distributed with µ = 3.6, σ = 1.5874
Then, P(x=5) ~ P(N<5.5) - P(N <4.5).

Answer 2

thank you

Answer 3

Yw!