Consider results of 20 randomly chosen people who have run a marathon. Their times, in minutes, are as follows: 136, 143, 153, 164, 166, 179, 184, 194, 199, 207, 216, 220, 228, 247, 252, 259, 275, 276, 282, 293 Calculate a 95% upper confidence bound on the mean time of the race. Assume distribution to be normal. Round your answer to the nearest integer (e. g. 9876) the absolute tolerance is +-1

And the confidence interval would be given by:

Step-by-step explanation:

Information given

136, 143, 153, 164, 166, 179, 184, 194, 199, 207, 216, 220, 228, 247, 252, 259, 275, 276, 282, 293

In order to calculate the mean and the sample deviation we can use the following formulas:  

(2)  

(3)  

represent the sample mean

population mean (variable of interest)

s=49.028 represent the sample standard deviation

n=20 represent the sample size  

Confidence interval

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

  (1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.95 or 95%, the value of and , and the critical value for this case is

And replacing we got:

And the confidence interval would be given by:

95.03 is the answer. hope this !