83 random samples were selected from a normally distributed population and were found to have a mean of 32.1 and a standard deviation of 2.4. Construct a 90% confidence interval for the population standard deviation.

Now we just take square root on both sides of the interval and we got:

Step-by-step explanation:

Information given

represent the sample mean

population mean (variable of interest)

s=2.4 represent the sample standard deviation

n=83 represent the sample size  

Confidence interval

The confidence interval for the population variance is given by the following formula:

The degrees of freedom given by:

The confidence level is 0.90 or 90%, the value of and , and we can use excel, a calculator or a table to find the critical values.  

The excel commands would be: "=CHISQ.INV(0.05,82)" "=CHISQ.INV(0.95,82)". so for this case the critical values are:

The confidence interval is given by:

Now we just take square root on both sides of the interval and we got:

b and c

step-by-step explanation:

answer: both chords and diameters have two endpoints on a circle. diameters must intersect the center of a circle.