The following measurements (in picocuries per liter) were recorded by a set of xenon gas detectors installed in a laboratory facility:

817.4,814.5,831.5,850.5,811.6,832.4 ,792.7

using these measurements, construct a 98% confidence interval for the mean level of xenon gas present in the facility. assume the population is approximately normal.

step 1 of 4: calculate the sample mean for the given sample data. round your answer to two decimal place

step 2 of 4: calculate the sample standard deviation for the given sample data. round your answer to two decimal places.

step 3 of 4: find the critical value that should be used in constructing the confidence interval. round your answer to three decimal places.

step 4 of 4: construct the 98% confidence interval. round your answer to two decimal places.

lower endpoint:

upper endpoint:

look at the picture i have filled out a table for it. hope this .

irst, find the z score of a score of 80. this is given by the formula z = (x-u)/o, where x is the score, u is the mean, and o is the standard deviation. this gives

z = (80-78)/12 = 1/6 = .1667

now, find what percentile a z score of 1/6 correlates to in the normal distribution.

a z score of 1/6 = .1667 is equivalent to the 56.36th percentile of the distribution. so the probability a score is over this is 1-.5636 = .4364

the mean of a sample mean is equal to the original mean. however, the standard deviation of a sample mean is equal to the original standard deviation divided by the square root of n (sample size). so the new standard deviation is 12/sqrt(16) = 3.

the new z score is 80-78/3 = 2/3 = .667. this is equivalent to the 74.86th percentile. so the probability that the mean will be greater than this score is 1-.7486 = .2514.