Question

The state test scores for 12 randomly selected high school seniors are shown on the right. Complete parts​ (a) through​ (c) below.

Assume the population is normally distributed.

1430	1223	985
691	727	833
725	748	540
624	1448	949

​(a) Find the sample mean.

x= _​ ​(Round to one decimal place as​ needed.)

​(b) Find the sample standard deviation.

s= _ ​(Round to one decimal place as​ needed.)​(c)

Construct a 99% confidence interval for the population mean is ​( _ ​, _ ​). (Round to one decimal place as​ needed.)

Answer 1

a) The sample mean is the simple average of all the data points

mean = (1430+1223+985+691+727+833+725+748+540+624+1448+949)/12 = 910.25

b) Sample standard deviation

We have to calculate standard deviation using the formula

==> SD = sqrt(((1430-910.25)^2 + (1223-910.25)^2 + (985-910.25)^2 + (691-910.25)^2 + (727-910.25)^2 + (833-910.25)^2 + (725-910.25)^2 + (748-910.25)^2 + (540-910.25)^2+ (624-910.25)^2 + (1448-910.25)^2 + (949-910.25)^2)/12) = 293.2

c) For 99%, the confidence interval = (mean - 2.576*SD, mean + 2.576*SD) = (910.25 - 2.576*293.2 , 910.25 + 2.576*293.2) = (155, 1665.5)