Question

Given an x value of 4, a mean of 2, and a standard deviation of 5, explain the steps that need to be used to find the area below and above this value of x, using a normal distribution table.  

Answer 1

With the given values of x, mean and standard deviation, calculate the z score using the formula,

z = (x - mean)/standard deviation

z = (4 - 2)/5

z = 0.4

In the standard normal distribution table, the probability value corresponding to the row 0.40 and column 0.00 gives the area below the value of x.

Area below x, P(x < 0.4) = 0.6554

Area above x, P(x > 0.4) = 1 - P(x < 0.4)

= 1 - 0.6554

= 0.3446