1. You are working with the following data set pertaining to the length of butterfly wings in a sample of butterflies: [10 marks]

Wing length (cm.)	Frequency
3.3	1
3.4	0
3.5	1
3.6	2
3.7	1
3.8	3
3.9	3
4.0	4
4.1	3
4.2	2
4.3	2
4.4	1
4.5	1

a)Calculate the arithmetic mean and the variance of this data.

b) Given your calculations of the mean and variance and given that the median = 3.975 cm, is this distribution normal? Explain.

c) Draw a histogram of this data with the Y-axis representing frequency and the X-axis representing wing length in cm.

d) What is the interval estimate of the population mean at a 95% confidence level? (z = 1.96)

e) What is the interval estimate of the population mean at a 99% confidence level? (z = 2.56)