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 3 inches. A random sample of 20 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 = = 3

n = 20

= = 15

= / n = 3/ 20 = 0.67

P(14.5 < < 15.5)  

= P[(14.5 - 15) / 0.67 < ( - ) / < (15.5 - 5) / 0.67 )]

= P( -0.75 < Z < 0.75)

= P(Z < 0.75) - P(Z < -0.75)

Using z table,  

= 0.7734 - 0.2266  

= 0.5468