You intend to estimate a population proportion with a confidence interval. The data suggests that the normal distribution is a reasonable approximation for the binomial distribution in this case. Find the critical value that corresponds to a confidence level of 99%.

The critical value that corresponds to a confidence level of 99% is, 2.58.

Step-by-step explanation:

Consider a random variable X that follows a Binomial distribution with parameters, sample size n and probability of success p.

It is provided that the distribution of proportion of random variable X, , can be approximated by the Normal distribution.

The mean of the distribution of proportion is,

The standard deviation of the distribution of proportion is, .

Then the confidence interval for the population proportion p is:

The confidence level is 99%.

The significance level is:

Compute the critical value as follows:

That is:

Use the z-table for the z-value.

For z = 2.58 the P (Z < z) = 0.995.

And for z = -2.58 the P (Z > z) = 0.005.

Thus, the critical value is, 2.58.

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