SOLUTION: 6. X has a normal distribution with a mean of 70.0 and a standard deviation of 3.0. Find the following probabilities: (A) P(x < 68.0) (B) P(68.0 < x < 72.0) (C) P(x>73.0)

Algebra ->  Probability-and-statistics -> SOLUTION: 6. X has a normal distribution with a mean of 70.0 and a standard deviation of 3.0. Find the following probabilities: (A) P(x < 68.0) (B) P(68.0 < x < 72.0) (C) P(x>73.0)       Log On


   

Question 309145: 6. X has a normal distribution with a mean of 70.0 and a standard deviation of 3.0. Find the following probabilities:

(A) P(x < 68.0)
(B) P(68.0 < x < 72.0)
(C) P(x>73.0)

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the z score for each x and use the normal distribution function.
a) x=68
z=%2868-70%29%2F3
z=-2%2F3
P%28z%29=0.2525
P(x<68.0)=0.253
.
.
.
b)x=72
z=2%2F3
P%282%2F3%29=0.7475
P(68.0 < x < 72.0) =P%282%2F3%29-P%28-2%2F3%29=0.7475-0.2525=0.495
.
.
.
c)x=73
z=1
P%281%29=0.8413
{P(x>73.0)=1-0.8413=0.159