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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 -

    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.

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