Question

A normal distribution has mean and standard deviation . Find the indicated probability for a randomly selected x-value from the distribution P (x > +3)

Answer 1

0.0228

Explanation:

Let us assume that the mean (μ) = 2 and the standard deviation (σ) = 0.5

Z score is a standard score used to measure the number of standard deviations by which the raw score (x) is above or below the mean. It is given by the equation:

`z=(x-\mu)/(\sigma)`

For x > 3

`z=(x-\mu)/(\sigma) =(3-2)/(0.5)=2`

From the normal distribution table, P(x > 3) = P(z > 2) = 1 - P(z < 2) = 1 - 0.9772 = 0.0228