SOLUTION: Determine the sample size for the following time study given a standard deviation of four minutes and a 98% probability that the value of the sample mean is within 1.5 minutes?

Click here to see ALL problems on Probability-and-statistics

Question 977142: Determine the sample size for the following time study given a standard deviation of four minutes
and a 98% probability that the value of the sample mean is within 1.5 minutes?
Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website!
A 98% confidence level corresponds to alpha = 0.02 and alpha/2 = 0.01
The region to the left of z(alpha/2) and to the right of z = 0, is 0.5 - .01 = 0.49.
**************************************************************************
In the table of the standard normal () distribution, an area of 0.49 corresponds to a value of 2.33.
The critical value is therefore z(alpha/2) = 2.33
***************************************************************************
The margin of error(E) = 1.5 and the standard deviation sigma = 4
let n be the sample size, then
n = ( (z(alpha/2) * sigma) / E )^2
n = ( (2.33 * 4) / 1.5 )^2
n = 38.60 approx 39
our sample size is 39