3. 125 points)Suppose the weight of a specific fish species is normally distribu

Question

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

Explanation / Answer

for normal distribution: z score =(X-mean)/std deviation

a) probbaility=P(X<10)=P(Z<(10-10)/2)=P(Z<0)=0.5

b)P(7<X<8.5)=P((7-10)/2<Z<(8.5-10)/2)=P(-1.5<Z<-0.75)=0.2266-0.0668 =0.1598

c)P(X>9)=1-P(X<9)=1-P(Z<(9-10)/2)=1-P(Z<-0.5)=1-0.3085=0.6915

d)probbaility that both fist are over 9lb=(0.6915)2 =0.4781

e) for 80th percentile ; zscore =0.8416

therfore corresponding fish weight =mean+z*std deviation=10+0.8416*2=11.68 lb

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