A normal population has a mean of 55 and a standard deviation of 14. You select a random sample of 25.?

A normal population has a mean of 55 and a standard deviation of 14. You select a random sample of 25. Compute the probability the sample mean is: (Round z values to 2 decimal places and final answers to 4 decimal places.)

(a) Greater than 59.

(b) Less than 54.

(c) Between 54 and 59.

1 Answer

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  • Mike G
    Lv 7
    5 months ago

    μ = 55

    σ = 14

    n = 25

    x̅ = sample mean

    a) z(x̅=59) = (59-55)/(14/√25)

    = 1.4286

    From the z-tables

    P(z>1.4286) =

    0.0764

    b) z(x̅=54) = (54-55)/(14/√25)

    = -0.3571

    P(z<-0.3571) =

    0.3594

    c) P(-0.3571<z<1.4286) =

    0.5642

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