Question

A large tank of fish from a hatchery is being delivered to a lake. The hatchery dams that the mean length of fish in the tank is 15 inches, and the standard deviation is 3 inches. A random sample of 46 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.) Need Help? Read It Talk to a Tutor

Answer 1

Here, μ = 15, σ = 0.4423, x1 = 14.5 and x2 = 15.5. We need to compute P(14.5<= X <= 15.5). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (14.5 - 15)/0.4423 = -1.13
z2 = (15.5 - 15)/0.4423 = 1.13

Therefore, we get
P(14.5 <= X <= 15.5) = P((15.5 - 15)/0.4423) <= z <= (15.5 - 15)/0.4423)
= P(-1.13 <= z <= 1.13) = P(z <= 1.13) - P(z <= -1.13)
= 0.8708 - 0.1292
= 0.7416

Ans: 0.7416