# In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a...

## Question:

In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 28 recent loans is taken. The average calculated from this sample is 5.25%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.50%. Compute 90% and 99% confidence intervals for the population mean 30-year fixed mortgage rate.

## Normal Distribution - Confidence intervals

If we have a normal distribution and we know the population standard deviation {eq}\sigma {/eq}, we can compute the confidence interval using the formula:

{eq}C=\displaystyle{\bar{x} \pm z \frac{\sigma}{\sqrt{n}}} {/eq},

where {eq}\bar{x} {/eq} is the sample mean, n is the number of sample, and the z score is obtained from a z table.

For a confidence level of 90%, {eq}z=1.645 {/eq} ,the confidence interval is then:

{eq}C=\displaystyle{\bar{x} \pm z \frac{\sigma}{\sqrt{n}}=5.25...

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