Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 6565 weekly reports showed a sample mean of 19.519.5 customer contacts per week. The sample standard deviation was 5.2.5.2. Provide 90%90% and 95%95% confidence intervals for the population mean number of weekly customer contacts for the sales personnel.

95% confidence

For the 90% confidence interval the critical value would be  and replacing we got:

represent the sample mean

population mean (variable of interest)

represent the sample standard deviation

n=65 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

  (1)

The degrees of freedom are given by:

Since the Confidence is 0.95 or 95%, the value of and , and the critical value would be

Now we have everything in order to replace into formula (1):

For the 90% confidence interval the critical value would be  and replacing we got:

answerthe vertex form

step-by-step explanation: