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Math Help - Normal distribution

  1. #1
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    Normal distribution

    If the average survival time of a red blood cell in the human body is 120 days with a standard deviation of 8 days, what percentage of the cells will survive for each of the following events: (using a normal distribution)

    a) BETWEEN 112 AND 128 DAYS

    b) more than 128 days

    c) less than 112 days

    d) at least 115 days

    e) less than 108 days

    Thank you.
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  2. #2
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    Quote Originally Posted by Hallah
    If the average survival time of a red blood cell in the human body is 120 days with a standard deviation of 8 days, what percentage of the cells will survive for each of the following events: (using a normal distribution)
    Thus, you know \sigma=8, \bar x=120

    Quote Originally Posted by Hallah
    a) BETWEEN 112 AND 128 DAYS
    Notice that 112=120-\sigma and 128=120+\sigma thus,
    P(112\leq x\leq 128)=.68

    Quote Originally Posted by Hallah
    b)more than 128 days
    Since, P(128\leq x)+P(x\leq 120)+P(120\leq x\leq 128)=1 You have, P(128\leq x)+.5+.34=1 thus, P(128\leq x)=.16
    Quote Originally Posted by Hallah
    c) less than 112 days
    Same idea as before thus, .16
    Quote Originally Posted by Hallah
    d) at least 115 days
    Since, P(115\leq x)=P(115\leq x\leq 120)+P(120\leq x) You have, (use z-score) P(115\leq x)=.23+.5=.73
    Quote Originally Posted by Hallah
    e) less than 108 days
    Same idea as before gives, .93
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  3. #3
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