Question

Using practical examples from the field of statistics, determine the following variables you expect to have a normal or nearly normal distribution. Illustrate by discussing and explaining possible reasons for your answer.

a. Scores on a very easy test

b. Shoe sizes of a random sample of adult women

c. The number of apples in each of 100 full bushel baskets

Answer 1

a) The scores here will follow Normal distrubution provided the sample size is large. This is because generally the scores are more clustered around the centre or mean values and there are very few scores with very low or very high values. So overall distribution is symmetric and Normal.

b) Shoe size will be nearly Normal. As shoe size will again be largely clustered around the mean. And there will be very few low or high sizes.

c) This may not be Normally distributed as here Number of apples may not be lying around the centre. This is a count data and might take Poisson distribution.