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March 28, 2017

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The average commute time via train from the Chicago O'Hare Airport to downtown is 60 minutes with a standard deviation of 15 minutes. Assume that the commute times are normally distributed. What proportion of commutes would be:

longer than 80 minutes?
less than 50 minutes?
between 45 and 75 minutes?

  • stat - ,

    Z = (score-mean)/SD

    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 calculated.

  • stat - ,

    a. Longer than 80 minutes?
    z(80) = (80-60)/15 = 4/3
    P(x> 80) = P(z> 4/3) = normal cdf(4/3,100) = 0.0912
    ---------------------------------------------------------
    b. Less than 50 minutes?
    z(50) = (50-60)/15 = -2/3
    P(x< 50) = P(z< -2/3) = normal cdf(-100,-2/3) = 0.2525
    ----------------------------------------
    c. Between 45 and 75 minutes?
    z(45) = (45-60)/15 =
    z(75) = (75-60)/15 =
    P (x=60) = P(z= ) = normal cdf (-100, ) =
    ----------------------

    ?

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