1) [1.5] For each problem, shade the correct area and find the numerical answer for each probability using the standard normal (z) distribution tables. a) P(Z > 0.41) b) P(0.18 -1.49) =. b) With dfn 17 and dfd = 9, find P(F < 0.57) = 6) [0.5] Given normal variable X~N( = 50.2, = 3.5), find P(X < 42.65). Show work. 7) [2] The average amount of money spent by a Target customer is $73.58 with standard deviation $29.80. Assume the variable is normally distributed. Answer the following questions. Show work. a) What is the probability that a Target customer spent more than $70? b) What is the probability that a Target customer spent between $75 and $100? 8) [1] If the average score of the MCA exam was 77 with standard deviation of 18.3, what is the probability a random sample of 10 students had an average score under 70? Assume the variable is normally distributed. Show work.