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Normal distribution to approximate binomial distribution

Decide whether the normal distribution can be used to approximate the binomial distribution. If it can, use the z-test to test the claim about the population proportion p for the given sample statistics and level of significance a.
^
A. Claim: p < 0.70; a = 0.01 Statistics: p = 0.50, n = 68
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B. Claim: p < 0.50; a = 0.10 Statistics: p = 0.71, n = 129

Test the claim about the indicated population parameter with ? a (X^2) -test using the given sample statistics and level of significance a. Assume the population is normally distributed.

A. Claim: ? ^2 ? 60 a = 0.025
Statistics: s?2 = 72.7, n = 15

B. Claim: ? ? 0.035: a = 0.01
Statistics: s = 0.026, n = 16

I have worked these several times but can't seem to get the answer. Thanks

Solution Preview

Hi there,

Thanks for letting me work on your post. Here is my explanation:

A. since np=68*0.50=34>5, nq=68*0.5=34>5, we could use the normal distribution can be used to approximate the binomial distribution.
Null hypothesis: p>=0.70
Alternative hypothesis: p<0.70
At 0.01 significance level, the critical z value is -2.326
test value ...

Solution Summary

The normal distribution to approximate binomial distributions are examined.

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