Asked by Kristin
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?
What is the probability that the average of this sample will be within 1.4 STANDARD ERRORS of the population mean?
Answers
Answered by
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 z-scores:
z = (x - mean)/sd
Therefore:
z = (66.2 - 67.6)/0.588 = -2.38
z = (69 - 67.6)/0.588 = 2.38
Finally:
Check z-table for the probability between the above two z-scores. This will be your answer.
I hope this helps.
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 z-scores:
z = (x - mean)/sd
Therefore:
z = (66.2 - 67.6)/0.588 = -2.38
z = (69 - 67.6)/0.588 = 2.38
Finally:
Check z-table for the probability between the above two z-scores. This will be your answer.
I hope this helps.
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