(28 points] 10 pounds and standard deviation of 2 pounds. If a fish of this spec
ID: 3364641 • Letter: #
Question
(28 points] 10 pounds and standard deviation of 2 pounds. If a fish of this species is caught randomly, what is the probability of the following events? 3. Suppose the weight of a specific fish species is normally distributed with mean of a. Weight of the fish is less than 10 pounds? b. Weight of the fish is in between 7 pounds and 8.5 pounds? If two fish are caught randomly, what is the probability that the weights of both fish will be more than 9 pounds? c. d. Calculate the 80th percentile of weights of this type of fish.Explanation / Answer
SolutionA:
mean=10
sd=2
P(X<10)
z=x-mean/sd
=10-10/2
=0
P(Z<0)
from standrad norma;l tables
P(Z<0)=0.5
ANSWER 0.5
Solutionb:
P(7<X<8.5)
P(7-10/2<Z<8.5-10/2)
=P(-1.5<z<-0.75)
From standard normal tables
P(-1.5<z<-0.75)=0.1598
ANSWER:0.1598
Solutionc:
n=2
P(X>9)
P(Z>9-10/2)/sqrt(2)
=P(Z>-0.71)
=P(Z<0.71)
=0.7611(from standard normal tables)
ANSWER :0.7611
Solutiond:
80h perecntile to z
Z=0.842
x-mean/sd=0.842
x-10/2=0.842
x-10=1.684
x=10+1.684
x=11.684
ANSWER:11.684
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