Question

Given the normally distributed variable x with mean 18 and standard deviation 2.5, find (a) p(x < 15), (b) the value of k such that p( x < k) = 0.2236

Answer 1

Part (a)

In this question we are asked to find the probability when x<15

Now it is given that X follows a normal distribution

Normal distribution is represented by z

z = (x - μ) / σ

We are given the values of mean and standard deviation

So we will get P ( Z < -1.2)

= 0.1151


Part (b)

The value of k such that P(x < k) = 0.2236

P ( Z < ( K – 18) / 2.5 ) = 0.2236

Z = -0.76

(k-18)/2.5 = - 0.76

k = 16.1


NOTE

Part b is the reverse question

We have to find out the value of k