# Homework Help: Probability of normal distribution

1. Oct 6, 2012

### g.lemaitre

1. The problem statement, all variables and given/known data

find the normal approximation for the binomial probability P(x = 4,5) where n=14 and p = .5.

2. Relevant equations

μ = np
σ = sqrt(npq)

z = (x - μ)/σ

3. The attempt at a solution

p = .5 q = .5

μ = 14*.5 = 7

σ = sqrt(14 * .5 * .5) = 1.87

z = (4 - 7)/1.87 = -1.61

(my book uses tables to convert the z score into the probability of getting x < 4)

z = -1.61 = .5 - .4463 = .0537

The book says the answer is .1812 which is not what i'm getting.

z =

2. Oct 6, 2012

### g.lemaitre

it's rare that such a simple problem takes this long. let me provide the example from the book

3. Oct 6, 2012

### Ray Vickson

The normal approximation is not very good in this example (because N = 25 is not very large and z is more than 2 standard deviations below the mean). P_exact = 0.0148904, while the continuity-corrected normal approximation is about 0.020152 (so using the normal gives about a 35% error). The normal approximation would be better if N were larger or z were closer to the mean.

RGV