A random variable is normally distributed with a mean of 25 and a standard deviation of 5. If an observation is randomly selected from the distribution, what value will be exceeded 85% of the time

Value of 26.93 will be exceeded 85% of the time.

Step-by-step explanation:

We are given that a random variable is normally distributed with a mean of 25 and a standard deviation of 5.

Let X = a random variable

So, X ~ N()

The z score probability distribution is given by;

            Z = ~ N(0,1)

where, = population mean

            = standard deviation

Now, we have to find that value which will be exceeded 85% of the time, i.e.;

        P(X > ) = 0.85

    1 - P(X ) = 0.85

         P(X ) = 0.15

         P( ) = 0.15

         P(Z ) = 0.15

Now, in the z table the critical value of whose less than area is 0.15 is given as 0.3853, i.e;

                  = 0.3853

                    = 25 + 1.9265 = 26.93

Therefore, value of 26.93 will be exceeded 85% of the time.

answer: x=3 and y=4

step-by-step explanation: