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?

statistics 
MathGuru,
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.