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 4inches. A random sample of 39 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:

We are given:

u = 15,0 = 4

We have to find:

P(14.5 < i < 15.5)

Using the z-score formula, we have:

14.5 - 15 P(14.5 < < 15.5) = P 4 <2< 15.5 - 15

= P(-0.7806 <=< 0.7806)

  

= Plz <0.7806) - P(Z < -0.7806)

Now using the standard normal table, we have:

$P(14.5< \bar{x}<15.5)=P(z<0.7806)-P(z<-0.7806)=0.7825-0.2175$

  $=0.5650$

Therefore, the probability that x is within 0.5 inch of the claimed population mean is 0.5650