1. 45% of koi fish (Cyprinus carpio) are orange, and the rest are multicolored.

Question

1. 45% of koi fish (Cyprinus carpio) are orange, and the rest are multicolored. Some of the species is infected with a particular virus, but that seems to vary by color. Only 10% of the orange fish have the virus, while 30% of the multicolored fish have the virus. Note: be sure to write your probability statements.

a. What is the probability of a multicolored koi fish? (1pt)

b. What is the overall probability of a koi fish having the virus? (2pts)

c. What is the probability of a multicolored fish being healthy? (1pt)

d. What is the probability of a healthy fish being multicolored? (2pts)

2. Adult Japanese Koi average 60.96cm ( = 5.31 cm), and their length follows a standard normal distribution. Note: be sure to write your probability statements and show your work.

a. What percent of the population is larger than 65 cm? (1.75pts)

b. 40% of the population is smaller than what size? (1.25pts)

c. What percent of the population is between 55 and 65 cm? (2.75pts)

d. 75% of the population is between 50cm and how many cm?

Explanation / Answer

2) Given that mean = 60.96 and sd = 5.31

a) P(X>65) , so we shall convert this into Z score using Z = (X-Mean)/SD

Z = (65 - 60.96)/5.31 = 0.7608

so P(Z>0.7608) , please keep the z tables handy now

P ( Z>0.7608 )=1P ( Z<0.7608 )=10.7764=0.2236 = 22.36%

b) in this we are given the z value and nwe need to solve for X

.4 = (X- 60.96)/5.31 , X = 0.4*5.31+60.96 = 63.08

c) P(55<X<65 ) , again converting this into z scores

Z = (65 - 60.96)/5.31 = 0.7608

Z = (55 - 60.96)/5.31 = -1.12

so P(-1.12<Z<0.7608) , now we know that

P (1.12<Z<0.7608 )=P ( Z<0.7608 )P (Z<1.12 )

After substituting a=1.12 we have:

P ( Z<1.12)=1P ( Z<1.12 )

P ( Z<1.12)=1P ( Z<1.12 )=10.8686=0.1314

At the end we have: P (1.12<Z<0.7608 )=0.645

d) Here we are given 0.75

so we need to calculate X such that

(X-60.96)/5.1-(50-60.96)/5.1 = 0.75 , solve for X

X-60.96)/5.1 = 0.75+2.14

= 2.8*5.1+60.96 = 75.24

Hope this helps !!

Please note that we can answer only 1 question ,with 4 subparts as per the answering guidelines

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