# Thread: Normal Distribution Problem -

1. ## Normal Distribution Problem -

Suppose X is a random variable with mean 3 and variance 4.
X1....X100 are independent random variables, each of which has the
same distribution as X. Let Y be the average of these variables (the sum divided by
100). Find a good approximation of P [|X-3|>0.5]?

my answer is 0.0124. Is that right?

2. Originally Posted by Yan
Suppose X is a random variable with mean 3 and variance 4.
X1....X100 are independent random variables, each of which has the
same distribution as X. Let Y be the average of these variables (the sum divided by
100). Find a good approximation of P [|X-3|>0.5]?

my answer is 0.0124. Is that right?
Yes

CB

3. Originally Posted by Yan
Suppose X is a random variable with mean 3 and variance 4.
X1....X100 are independent random variables, each of which has the
same distribution as X. Let Y be the average of these variables (the sum divided by
100). Find a good approximation of P [|X-3|>0.5]?

my answer is 0.0124. Is that right?
You mean P [|Y-3|>0.5]=1-P(2.5<Y<3.5)

where Y is approximately normal with mean 3 and st dev 1/5.