MSA 8190Statistical FoundationsFall 2021Practice Problems 3Note: Make sure to clearly define the random variables and specify their probabilitydistributions and parameters.Use R for computations in the following questions.Problem 1Suppose the time it takes a data collection operator to fill out an electronic form for adatabase is uniformly between 1.5 and 2.2 minutes.(a) What is the mean and variance of the time it takes an operator to fill out the form?(b) What is the probability that it will take less than two minutes to fill out the form?(c) Determine the cumulative distribution function of the time it takes to fill out the form.Problem 2AssumeZhas a standard normal distribution. Determine the value forzthat solves each ofthe following:(a)P(Z < z) = 0.9(b)P(Z < z) = 0.5(c)P(Z > z) = 0.1(d)P(Z > z) = 0.9Problem 3The fill volume of an automated filling machine used for filling cans of carbonated beverageis normally distributed with a mean of 12.4 fluid ounces and a standard deviation of 0.1 fluidounce.(a) What is the probability a fill volume is less than 12 fluid ounces?(b) If all cans less than 12.1 or greater than 12.6 ounces are scrapped, what proportion ofcans is scrapped?(c) Determine specifications that are symmetric about the mean that include 99% of allcans.