Statistics- Binomial PDF

Question

A binomial probability experiment is conducted with the given parameters.

n=55, p=0.75

Find probability when p(35<x<41)

Round your answer to nearest ten-thousandth if necessary.

Answer 1

mean = np = 41.25

standard deviation = sqrt(n*p*(1-p)) = 3.21

apply normal approximation:

z = (x - mean)/SD has mean 0 and standard deviation 1.

so P(35 < x < 41) = P( (35-41.25)/3.21 < z <(41-41.25)/3.21)) = P(-1.95 < z < -0.078) = P(z < -0.078) - P(z < -1.95).

use standard normal probabilities table to compute probabilities.