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. 1425 1227 989 697 729 839 729 742 550 626 1449 941 (a) find the sample mean. x overbarequals nothing (round to one decimal place as needed.) (b) find the sample standard deviation. sequals nothing (round to one decimal place as needed.) (c) construct a 95% confidence interval for the population mean mu. a 95% confidence interval for the population mean is ( nothing, nothing). (round to one decimal place as needed.)

A) 
B) s = 304.2
C) 

To find the sample mean, add all of the data points together and then divide by 12, the number of data points:
(1425+1227+989+697+729+839+729+742+550+626+1449+941)/12 = 10943/12 = 911.9

To find the sample standard deviation, subtract each data point from the mean; square the result; find the average of these; then take the square root.

To construct a confidence interval, first find the z-score that goes along with it:
Convert 95% to a decimal:  0.95
Subtract from 1:  1-0.95 = 0.05
Divide by 2:  0.05/2 = 0.025
Subtract from 1:  1-0.025 = 0.975

Using a z-table (http://www.z-table.com) we see that this value corresponds with a z-score of 1.96.

We use this to calculate the margin of error:


This gives us the confidence interval

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