1. GCSE Statistics
Normal Distribution

2. 20 November November 2018
The normal distribution
This is a continuous distribution. This means that it applies to continuous data only. It generally occurs as a result of a natural process, such as height and weight of people or circumferences of apples.
It is a bell-shaped distribution where the area under the bell represents the probability of the occurrence of the whole distribution. Thus the area is 1.

3. To compare normal distributions use the mean and standard deviation.
What comments can you make about these distributions?

4. Important properties
the distribution is symmetrical about the mean μ
the mean, mode and median are all equal
95% of the observations lie within ± 2 standard deviations (σ) of the mean
almost all (99.8%) of the observations lie within ± 3 standard deviations of the mean

5. Sketching a normal distribution (this is worth up to 5 marks!)
Sketch 3 standard deviations either side of the mean
Mark the value and number of standard deviations on the scale
Example
Jam is packed in tins of weight 1kg. The weight of the tins is normally distributed with a standard deviation of 10g.
Work out the percentage of tins that lie between 980g and 1020g
Between what weights will almost all the tins lie?

6. Example 2
Students travelling to college take a mean time of 20 minutes. The times are normally distributed with standard deviation 3.5 minutes.
Calculate the percentage of students that take more than 27 minutes to get to college
There are 800 students in the college
b) Work out how many take less than 13 minutes to get to college

7. Comparing 2 normal distributions (this is worth up to 5 marks!)
Sketch 3 standard deviations either side of the mean
Mark the values on the scale
Remember both have the same area, so the curve with the greater standard deviation will be shorter.
Example 5 in book page 104.
1 mark for labelling each curve and for a scale on the axis
1 mark for correct spreads
2 marks for using mean (one for each curve)
1 mark for different heights

8. The table gives some information about the distribution of the weights (g) of two types of rodent. The weights are normally distributed.
Sketch on the same axes the normal curves for these two distributions
Rodent A
Rodent B
Mean µ
800g
500g
Standard deviation σ 25 50

9. Example 8 page 306
A long-life bulb has a mean life of hours and a standard deviation of 300 hours.
Work out the probability that a light bulb chosen at random will
last between hours and hours
Last less than hours
5000 light bulbs are tested. Estimate how many of them would last longer than hours
Sketch a picture of what is happening
The text uses:
number of standard deviations = 𝒗𝒂𝒍𝒖𝒆 −𝒎𝒆𝒂𝒏 𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅 𝒅𝒆𝒗𝒊𝒂𝒕𝒊𝒐𝒏 to help with part a
And then answer the questions

10. Your turn
Exercise 8D page 307