ote Suppose the weight of a specifie fish species is normally distributed with a

Question

ote Suppose the weight of a specifie fish species is normally distributed with an of o lb, and standard deviation of 2 lb. If a fish of this specie is randomly caught, what specific fish species is normally distributed with the weight of is the probability of the following events? Weight of the fish is less than 10 lb.? 3, 125 points) a. b. Weight of the fish is between 7 1b. and 8.5 tb. c. Weight of the fish is more than 9 lb. d. If two of the fish are randomly caught, what is the probability that both of the fish weight are over 9 Ib.? e. Calculate the 80h percentile of a fish of this type.

Explanation / Answer

Mean = 10 lb

Standard deviation = 2 lb

P(X < A) = P(Z < (A - mean)/standard deviation)

a) P(weight is less than 10 lb) = 0.5

b) P(weight is between 7lb and 8.5 lb) = P(X < 8.5) - P(X < 7)

= P(Z < (8.5-10)/2) - P(Z < (7-10)/2)

= P(Z < -0.75) - P(Z < -1.5)

= 0.2266 - 0.0668

= 0.1598

c) P(weight is more than 9 lb) = P(X > 9)

= 1 - P(X < 9)

= 1 - P(Z < (9 - 10)/2)

= 1 - P(Z < -0.5)

= 1 - 0.3085

= 0.6915

d) P(both fishes are over 9 lb) = 0.69152

= 0.4782

e) Let P denote the 80th percentile

P(X < P) = 0.8

P(Z < (P - 10)/2) = 0.8

From the standard normal distribution table,

(P - 10)/2 = 0.84

P = 11.68

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