SOLUTION: Please help me solve this problem. If X is Normally distributed with a mean of 3 and a variance of 4, find P(|X−3|>1.7) to 2 decimal places. Thank you!

Algebra ->  Probability-and-statistics -> SOLUTION: Please help me solve this problem. If X is Normally distributed with a mean of 3 and a variance of 4, find P(|X−3|>1.7) to 2 decimal places. Thank you!      Log On


   

Question 973142: Please help me solve this problem.
If X is Normally distributed with a mean of 3 and a variance of 4, find P(|X−3|>1.7) to 2 decimal places.
Thank you!
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
mean of X=3
SD =2 (variance is 4); Would expect most of the values to be within 1 and 5
x> 4.7
x<1.3
Both of those satisfy (|X−3|>1.7 ;;;;x-3>1.7; x>4.7 ;;; x-3 < -1.7; x<1.3
z+(x-mean)/2 = (1.7)/2 z> +0.85
z=(1.3-3)/2 =- (1.7)/2 z< -0.85
P= 0.40 This seems reasonable.