Statistics: The CLT

Question

A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 6 inches. A random sample of 22 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)

Answer 1

will use standardized normal z stat for mean = (xbar - population mean)/(standard deviation/square root(sample size).

z = (xbar - 15)/(6/sqrt(22))

P(14.5 < xbar < 15.5) = P( (14.5 - 15)/(6/sqrt(22) < z < (15.5 - 15)/(6/sqrt(22) = P(-0.39 < z < 0.39) = P(z < 0.39) - P(z < -0.39) = 0.6517 - 0.3483 = 0.3034