statistics

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random sample of n = 16 scores is selected from a normal distribution with a mean of μ = 50 and standard deviation of σ = 10.
a. what is the probability that the sample mean will have a value between 45 and 55?
b. what is the probability that the sample mean will have a value between 48 and 52?
c. what range of values contains the middle 95% of all possible sample means for n = 16?

  • statistics -

    Find z-scores using sample size:

    z = (x - mean)/(sd/√n)

    For a):
    x = 45, 55
    mean = 50
    sd = 10
    n = 16

    Find two z-scores, using the values above. Use a z-table to find the probability between the two scores.

    For b):
    x = 48, 52
    mean = 50
    sd = 10
    n = 16

    Find two z-scores, using the values above. Use a z-table to find the probability between the two scores.

    For c):
    -1.96 = (x - 50)/(10/√16)
    1.96 = (x - 50)/(10/√16)

    Solve both equations for x. Those values will be your range of values containing the middle 95%.

    I hope this will help get you started.

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