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Question 7 In a manufacturing process where glass products are produced, defects or bubbles occur, occasionally rendering the piece undesirable for marketing. It is known that, the number of defects follow a Poisson process and on average 4 of these items produced on a given day has one or more bubbles. Let X denote the number of days until 25 items with one or more bubbles are produced. (12 pts.) Parta) What is the distribution of X and what are its parameters? Is this a valid probability density function? (1 pts) Part b) Find the probability that X exceeds 14 days. Illustrate the desired probability on the pdf plot. Calculate the probability also by using Poisson distribution. Plot also the pmf of the corresponding Poisson random variable. (2 pts.) Part C) Find the probability that X is between 13 and 18 days. Illustrate the desired probability on the pdf plot Calculate the probability also by using Poisson distribution. (1 pts) Part d) Calculate the mean variance and standard deviation of X. (2 pts.) Parte Find the probability that X exceeds 14 days using normal approximation illustrate the desired probability on the normal pdf plot (2 pts) Part 1) Find the probability that X is between 13 and 18 days using normal approximation. Illustrate the desired probability on the normal pdf plot. (2 pts) Part g) Compare the results obtained without using approximation and the results obtained by using normal approximation is this problem suitable for applying normal approximation? (2 pts)