When working with the normal distribution you will need to be able to calculate probabilities.

It is important that you are able to use the tables correctly and this is generally where I find that people go wrong. In the tutorials that follow I try to show you how to handle the various possible situations that you may come across.

Finding the P(X<x) where x>mean

(1) A battery has a lifetimes which are normally distributed with a mean of 62 hours and a standard deviation of 3 hours. What is the probability of a battery lasting less than 68 hours?

Tutorial and Worked solution to (1)

 

Finding the P(X>x) where x>mean

(2) The masses of a well known brand of breakfast cerial are normally distributed with mean of 250g and standard deviation of 4g. Find the probability of a packet containing more than 254.4g.

Tutorial and Worked solution to (2)

 

Finding the P(X>x) where x<mean

(3) A carton of orange juice has a volume which is normally distributed with a mean of 120ml and a standard deviation of 1.8ml. Find the probability that the volume is more than 118ml.

Tutorial and Worked solution to (3)

 

Finding P(X<x) where x<mean

(4) A light bulb has lifetimes which are distributed with a mean of 520 hours and a standard deviation of 6 hours. What is the probability of a light bulb lasting less than 511 hours?

Tutorial and Worked solution to (4)

 

Calculating the Mean and Standard Deviation

You can also be expected to calculate the mean and standard deviation of a normal distribution.

How to calculate the mean and standard deviation