# Math Help - Normal distribution

1. ## 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.

2. 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 $\sigma=8$, $\bar x=120$

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

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, $P(128\leq x)=.16$
Originally Posted by Hallah
c) less than 112 days
Same idea as before thus, .16
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) $P(115\leq x)=.23+.5=.73$
Originally Posted by Hallah
e) less than 108 days
Same idea as before gives, .93

3. ## Thank You

Thank you for ALL your help. I need you teaching my class.