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 5inches. A random sample of 47 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

Solution :

Given that,

mean = = 15

standard deviation = = 5

n = 47

= = 15

= / n = 5/47 = 0.7293

P( 14.5 < < 15.5) = P((14.5 - 15) / 0.7293 < ( - ) / < (15.5 - 15) / 0.7293))

= P(-0.69 < Z < 0.69)

= P(Z < 69) - P(Z < -0.69) Using z table,

= 0.7549 - 0.2451

= 0.5098

The probability that x is within 0.5 inch of the claimed population mean is 0.5098.