Suppose X~N(22.8, 2.15) and P(x > 20)=.87

Question

What is the value of z?

Answer 1

To find the value of z, we need to standardize the value of x using the formula:

z = (x - μ) / σ

Where:
x is the given value (20 in this case)
μ is the mean of the distribution (22.8)
σ is the standard deviation of the distribution (2.15)

Now calculate the z-score:

z = (20 - 22.8) / 2.15
z = -2.8 / 2.15
z ≈ -1.30

So, the value of z is approximately -1.30.