Question

What conditions need to be satisfied to use the normal approximation for proportions? Use an example if necessary. Remember to comment on your classmates posts.

Answer 1

Solution:

As the normal approximation is generally not accurate for any smaller values of 'n', The thumb rule that can be used for normal approximation is np > 5 and n(1-p) > 5.

For example,

Consider a village with 200 people. Out of them 40% are diseased.

Here, p = 0.4 (40% = 40/100 = 0.4)

n = 200

So,

np = 0.4 * 200 = 80

n(1-p) = (1 - 0.4) * 200 = 120

As for both the cases np and n(1-p) are more than 5, so it is normally distributed.

End..

(OR)   

In order to use normal approximation for proportion following 2 conditions need to be satisfied.

1. N should be sufficiently large.

2. Proportion should be close to 0.5

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