Page 1 of 5 Must show all your work step by step in order to receive the full credit; Excel is not allowed. 55.The random variable x has a normal distribution with mean 50 and variance 9. Find the value of X, call it X0, such that: a) P (X x0) = 0.8413 b) P (X > X0) = 0.025 c) P (X > X0) = 0.95 d) P (41 X x0) = 0.8630 Page 2 of 5 56.The random variable x has a normal distribution with - 40 and 2 = 36. Find the value of X, call it X0, such that: b) P ( X < X0 ) = 0.05 a) P ( X X0 ) = 0.10 ) P ( X X0 ) = 0.40 Page 3 of 5 57.A sample of size n = 10 is randomly selected from a normal population with 2 mean = 52 and variance = 22.5. The sample value X is calculated. a) P ( X >55 )=? c) P ( X 55 ) =? b) P ( 50 X 60 )=? Page 4 of 5 58.Consider the following data drawn from a normal distribution population: 4, 8, 12, 11, 14, 6, 12, 8, 9, 5 Construct a 90% confidence interval for the population mean. a) Mean b) Variance c) Standard deviation d) Find a 90% confidence interval for the mean . Interpret this interval Page 5 of 5