You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 63. While it is an uncommon confidence interval, find the critical valuebthat corresponds tona confidence interval of 81.2%.

The critical value that corresponds to a confidence interval of 81.2% is 1.32.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.  

Then, the mean of the sample means is given by,

And the standard deviation of the sample means is given by,

In this case the sample selected is of size, n = 63.

As the sample size n = 63 > 30, the sampling distribution of sample mean will be approximately normal.

So, a z-interval will be used to estimate the population mean.

The confidence level is, 81.2%.

The value of α is:

The critical value is:

*Use a z-table.

Thus, the critical value that corresponds to a confidence interval of 81.2% is 1.32.

m∠a is 90°

m∠b is 40°