# Normal distribution

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• April 7th 2006, 09:45 PM
Hallah
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.
• April 8th 2006, 06:32 PM
ThePerfectHacker
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
• April 8th 2006, 10:36 PM
Hallah_az
Thank You
Thank you for ALL your help. I need you teaching my class.