statistics
posted by Kristin on .
The average temperature in households is 67.6 degrees F. The standard deviation is 4.2 degrees F. A random sample of 51 households is to be selected
What is the probability that the average of this sample will be within 1.4 STANDARD ERRORS of the population mean?

mean = 67.6
standard deviation = 4.2
sample size = 51
Standard error: sd/√n = 4.2/√51 = 0.588
Next step:
67.6  1.4 = 66.2
67.6 + 1.4 = 69
Use zscores:
z = (x  mean)/sd
Therefore:
z = (66.2  67.6)/0.588 = 2.38
z = (69  67.6)/0.588 = 2.38
Finally:
Check ztable for the probability between the above two zscores. This will be your answer.
I hope this helps.