Question

The weight of trout in a fish farm follows the distribution N(200,502). A trout is randomly selected. (a) What is the probability that its weight does not exceed 175g? (b) What is the probability that its weight is greater than 230g? (c) What is the probability that its weight is between 225g and 275g? (d) What is the probability that out of eight trout selected randomly from the fish farm, less than three of them will not weigh more than 175g?

Answer 1

Part a)

P ( X < 175 )
Standardizing the value

Z = ( 175 - 200 ) / 22.4054
Z = -1.12

P ( X < 175 ) = P ( Z < -1.12 )
P ( X < 175 ) = 0.1314

Part b)

P ( X > 230 ) = 1 - P ( X < 230 )
Standardizing the value

Z = ( 230 - 200 ) / 22.4054
Z = 1.34

P ( Z > 1.34 )
P ( X > 230 ) = 1 - P ( Z < 1.34 )
P ( X > 230 ) = 1 - 0.9099
P ( X > 230 ) = 0.0901

Part c)

P ( 225 < X < 275 )
Standardizing the value

Z = ( 225 - 200 ) / 22.4054
Z = 1.12
Z = ( 275 - 200 ) / 22.4054
Z = 3.35
P ( 1.12 < Z < 3.35 )
P ( 225 < X < 275 ) = P ( Z < 3.35 ) - P ( Z < 1.12 )
P ( 225 < X < 275 ) = 0.9996 - 0.8677
P ( 225 < X < 275 ) = 0.1318

Part d)

Probability mass function of Binomial distribution is

P ( X < 3 ) = 0.9237