A producer of printed circuit boards (PCBs) wishes to estimate the scoring depth of their circuits. To this end, they have collected 45 samples of measured depths. The mean and standard deviations of these samples is 0.165 mm and 0.022 mm respectively.

1. Create a plot showing the dependence of the size of the confidence interval (ρ) on the confidence level (γ) ranging from 0 to 1. Keep the sample size fixed at 45

2. Create a plot showing the dependence of the size of the confidence interval on the
sample size ranging from 1 to 100. Keep the confidence level fixed at 0.95. (Here you
can assume normality even where N <30)

3. Create a plot showing the pdf of the sample mean and with the area computed above shaded in. Hint: plt.fill between.