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 2 inches. A random sample of 49 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 = = 2

n = 49

=   = 15

= / n = 2 / 48 = 0.286

P(14.5 < < 15.5)  

= P[(14.5 - 15) /0.286 < ( - ) / < (15.5 - 15) / 0.286 )]

= P( -1.75 < Z < 1.75)

= P(Z < 1.75) - P(Z < -1.75)

Using z table,  

= 0.9599 - 0.0401

= 0.9198