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 46 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?

0.4246

Step-by-step explanation:

Given data:

mean ( u ) = 15 inches

std ( б )= 6 inches

sample size( n ) = 46

ux = mean sample length

Determine the probability that x within 0.5 inch of the claimed population mean

ux = u = 15

бx = б/ √ 46 =  6 /√ 46 = 6 / 6.78 = 0.88

Hence the   P( 14.5 < x < 15.5 )

= P ( [14.5 - 15 / 0.88 ] < z < (15.5 - 15) / 0.88) )

= P ( -0.5682 < z <  0.5682 )

= P ( z < 0.5682 ) - P ( z < -0.5682 )

= 0.7123 - 0.2877  ( from Z table )

= 0.4246

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step-by-step explanation: