Question

In: Statistics and Probability

A large tank of fish from a hatchery is being delivered to a lake. The hatchery...

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 6 inches. A random sample of 60 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?

a. .5000

b. .4814

c. .1467

d. .0325

Solutions

Expert Solution

Solution :

Given that,

mean = = 15

standard deviation = = 6

n = 60

= = 15

= / n = 6 / 60 = 0.7746

P(14.5 < < 15.5)  

= P[(14.5 - 15) /0.7746 < ( - ) / < (15.5 - 15) / 0.7746)]

= P(-0.6455 < Z < 0.6455)

= P(Z < 0.6455) - P(Z < -0.6455)

Using z table,  

= 0.7407 - 0.2593  

= 0.4814

correct option is = b

orchestra answered 2 years ago
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