The following data are the temperatures (in °F) of effluent at discharge from a sewage treatment facility on consecutive days: 43 47 51 48 52 50 46 49 45 52 46 51 44 49 46 51 59 45 44 50 48 50 49 50
a. Construct the experimental (empirical) cumulative distribution of the data. Using the experimental CDF:
i. Find the probability that temperature exceeds 58 oF?
ii. Find the temperature value that is exceeded only 5% of the time.
Using the method of moments, fit a normal distribution, a lognormal distribution, a gamma distribution, an exponential distribution, a beta distribution, and a uniform distribution and provide the following for each distribution:
i. Parameters of the distribution.
ii. Using the fitted distribution, find the probability that temperature exceeds 58 oF?
iii. Using the fitted distribution, find the temperature value that is exceeded only 5% of the time.
iv. Construct probability plots for the normal, lognormal, and gamma distributions (you can use the "probplot" function in MATLAB). Based on visual evaluation, do these distributions fit the temperature data?