Question

A normally distributed population has a mean of 475 and a standard deviation of 48. a. Determine the probability that a random sample of size 9 selected from this population will have a sample mean less than 451. b. Determine the probability that a random sample of size 16 selected from the population will have a sample mean greater than or equal to 498. a. P(X<451) = (Round to four decimal places as needed.) b. P(X2498) = 1 (Round to four decimal places as needed.)

Answer 1

Solution given that M= 475 6= 48 (a) n=9 = With p(x (451) =P = 48/9 = 16 8-4 451-445 6Nn - 48 Ng =P (22-24) 16 - P 24-1.5) - 0.0668 probability = 0.0668 [using z table] In = 16 6 11th = 4 NT6 = 12 p(x7470) = 1 olshñ - 498475 48 INTO = 1- P (2c 1.92) - 1-0.9726 = 0.0274 Probability = 0.0274 [using z table]