GCSE Statistics Normal Distribution January 2022 The normal

GCSE Statistics Normal Distribution

January 2022 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.

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

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

Sketching a normal distribution (this is worth up to 5 marks!) 1. Sketch 3 standard deviations either side of the mean 2. Mark the value and number of standard deviations on the scale Example Jam is packed in tins of weight 1 kg. The weight of the tins is normally distributed with a standard deviation of 10 g. a) Work out the percentage of tins that lie between 980 g and 1020 g b) Between what weights will almost all the tins lie?

Example 2 Students travelling to college take a mean time of 20 minutes. The times are normally distributed with standard deviation 3. 5 minutes. a) 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

Comparing 2 normal distributions (this is worth up to 5 marks!) 1. Sketch 3 standard deviations either side of the mean 2. Mark the values on the scale 3. 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

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

Your turn Exercise 8 D page 307