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In: Math

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 4 inches. A random sample of 28 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.)

Solutions

Expert Solution

Solution :

Given that,

mean = = 15

standard deviation = = 4

n = 28

=

= / n = 4 / 28 = 0.76

P(14.5< < 15.5 )  

= P[(14.5 -15) / 0.76 < ( - ) / < (15.5 - 15) / 0.76 )]

= P(- 0.66 < Z < 0.66)

= P(Z < 0.66 ) - P(Z < - 0.66)

Using z table,  

= 0.7454 - 0.2546

= 0.4908

milcah answered 10 months ago
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