Pacific Beverages, a large juice manufacturing company, bottles orange juice with 10 bottling machines. A sample of 500 days yielded the following data: Number of machine failures 0 1 2 3 4 5 6 7 8 No of days observed 50 75 25 100 50 75 50 25 50 (a) Based on the above data, construct the probability distribution of the random variable X = the number of machine failures on a given day. Draw a graph of the distribution. (b) Find the variance and standard deviation of X. (c) What is the probability of at least 2 machine failures on any day? (d) What is the probability of more than 4 machine failures on any given day