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The population of SAT scores forms a normal distribution with a mean of µ =500 and a standard deviation of σ =100. If the average SAT score calculated for a sample of n = 25 students,
a. What is the probability that the sample mean will be greater than M= 510. In symbols, what is p (M >520?
b. What is the probability that the sample mean will be greater than M = 520. In symbols, what is p (M>520?
c. What is the probability that the sample mean will be between M =510 and M = 520? In symbols, what is p (510 < M < 520?

  • statistics -

    Z = (mean1 - mean2)/standard error (SE) of difference between means

    SEdiff = √(SEmean1^2 + SEmean2^2)

    SEm = SD/√(n-1)

    If only one SD is provided, you can use just that to determine SEdiff.

    Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to the Z scores.

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