Probability of normal distribution

[g.lemaitre]

Homework Statement

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

Homework Equations

μ = np
σ = sqrt(npq)

z = (x - μ)/σ

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 =

 

[g.lemaitre]

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

 

[Ray Vickson]

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

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