A wooden kitchen cabinet is carefully inspected at the manufacturing facility before it is sent to a retailer. The random variable X is the number of defects found in a randomly selected cabinet. The probability distribution for X is given in the following table. Please use at least three decimal places in this question. Suppose that a cabinet is selected at random. x 0 1 2 3 4 5p(x) 0.9 0.05 0.025 0.016 0.003 0.006a. Find the variance and standard deviation of X. Hint: The computational formula. b.If the number of defects found is more than one standard deviation above the mean, the manufacturing facility needs to recalibrate their machines. What is the probability that the facility needs to recalibrate their machines?c. Suppose the random variable W is defined by W = X^2 - 5. Find the mean of W. d. Suppose two cabinets are selected at random. What is the probability that each of the two cabinets has fewer than three defects?