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The average middle-distance runner at a local high school runs the mile in 4.5 minutes, with astandard deviation of 0.3 minute. What is the probability that a runner will run the mile in less than 4 minutes?

Possible Answers:
A)7%B)3%C)5%D)4%

I know it's C, but I don't know how to get it.

Can someone please show me a step by step solution, please. I am completely lost.

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  1. 4 min is .5 min below the mean ... 1.667 standard deviations

    -1.667 is called the z-score

    a z-score table will show the fraction of the population at or below this point

    the table actually shows about 4.8%

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  2. Best normal distribution applet on line:
    http://davidmlane.com/normal.html
    enter:
    mean : 4.5
    SD : 0.5
    click on below, enter 4 to get .047799..
    or 4.8% as Scott stated.

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