Suppose X is a random variable from the normal distribution

Suppose X is a random variable from the normal distribution with mean 0f 1.8 and unknown standard deviation. Furthermore, let P(1.6<x<2.0) = 0.72. Is it possible to determine the exact value of P(x>1.6)? If yes calculate it, if not explain why not.

Solution

Yes, normal distribution is symmetric about mean 1.8, so area from 1.6 to 2.0 = 0.72, which is symmetric, so area outside this range = 1 - 0.72 = 0.28, and P(X<1.6) = 0.28/2 = 0.14 (because the two 1.6 and 2.0 are equidistant form mean)

thus P(X>1.6) = 1 - 0.14 = 0.86