Question: Question 1: Data contains observations (in parts per million, ppm) of the level of carbon monoxide (CO) in air samples taken close to the centre of 16 British cities.

(a) Produce a dot plot of the data. On the dot plot, indicate the position of the lower quartile, the median and the upper quartile.

(b) Show that a lognormal distribution gives a better fit to the data than a normal distribution.

(c) Using the data to estimate the parameters of the lognormal distribution. Calculate the probability of observing a level of CO (i) less than 5 ppm (ii)) greater than 15 ppm (iii) between 7.5 and 10 ppm.

(d) Take natural logs (logs to base e) of the data and calculate a 95% confidence interval for the mean of the lognormal distribution. Transform the lower and upper confidence limits back to the original scale (ppm) and indicate their positions on your dot plot.