Question

Assuming the population is normally distributed, find the probability P(x>4.5) given the mean is 6 and the standard deviation is 0.7

Answer 1

`P(x > 4.5)= 0.983943`

Explanation:

Given

`\mu = 6`

`\sigma = 0.7`

Required

`P(x > 4.5)`

Start by calculating the z score

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

So:

`z = (4.5 - 6)/(0.7)`

`z = (-1.5)/(0.7)`

`z = -2.143`

So, we have:

`P(x > 4.5)= 1 - P(x < 4.5)`

This gives:

`P(x > 4.5)= 1 - P(x < z)`

`P(x > 4.5)= 1 - P(x < -2.143)`

Using the z score probability table, we have:

`P(x > 4.5)= 1 - 0.016057`

`P(x > 4.5)= 0.983943`