CONTINUOUS RANDOM VARIABLE PLEASE HELP

Question

A continuous random variable is normally distributed. The probability that a value in the distribution is greater than 56 is 0.6387. Find that probability that a value in the distribution is less than 56.

Answer 1

Let X be the name of the random variable.

We are given

P(X>56) = 0.6387.

The general fact that the total probability of all events is 1:

P(X<56) + P(X=56) + P(X>56) = 1

P(X<56) = 1 - P(X=56) - P(X>56) = 1 - 0.6387 = 0.3613

We used the given information that X is continuous in getting P(X=56) = 0.

We did not use the given information that X is normally distributed;

this result is true for any distribution.