You are analyzing the probability of defective machine parts coming out of an assembly line. Data collected over 60 consecutive days, revealed 2 days where defects were observed in machine parts. To assess the uncertainty of the probability estimate , calculate the posterior probability distribution using a non-informative prior [ p ( ) = 1 p()=1] and steps of 0.001. You must ensure the area under the posterior probability function is equal to 1.

Check to see if the distribution of the parameter can be approximated by the normal distribution. Yes or no and why?

Explain how to calculate confidence intervals for whether the approximation is valid or not.

Solve clearly