Question

Given a random variable X follows a Normal distribution with mean 10 and standard deviation 5, what is the probability that X lies within one standard deviation of the mean?

a) 0.4722
b) 0.9005
c) 0.6827
d) 0.9545

Answer 1

c) 0.6827

Explanation:

We have to find P(-1<Z<1) by using z-table

P(-1<Z<1) = P(Z<1) – P(Z<-1)

P(-1<Z<1) = 0.841345 - 0.158655

P(-1<Z<1) = 0.682689

P(-1<Z<1) = 0.6827