1. It is known that of 1000 units of ACME cars of a lot of 8000, are red. If 400

Question

1. It is known that of 1000 units of ACME cars of a lot of 8000, are red. If 400 cars were sent to a dealer What is the probability that he receives a hundred or less red cars? (Asuma X = auto red color)

a. P (X <= 100) =? (Hypergeometric)

b. P (X> 50) =?

c. E (x) = expected value of red cars

2. It is known that ACME cars from a batch of 200. There are 40 radio units damaged, 60 defective batteries. If 20 cars were sent to a dealer. (Hypergeometric)

a. What is the probability that you will receive 3 with defective radios? P (X = 3 | N = 200, A = 40, n = 20)

b. What is the probability that you will receive 3.0 or more with defective batteries?

c. In the long run, how many cars with defective batteries will be observed in a sample of 200?

3. It is known that of 1000 units of ACME cars of a lot of 5000, they are red; 1500 are blue. If 400 cars were sent to a dealer. Determine the following probabilities: (Assume X = auto red for items a and b) a. P (X> = 100) =? b. P (X <50) =? c. E (x) = expected value of blue car cars

Explanation / Answer

from hypergeomteric distribution

1) a) P(X<=100) = 0100 (1000Cx )*(7000C400-x )/(8000C400 )=1.0000

P (X> 50) =1-P(X<=50) =1- 050 (1000Cx )*(7000C50-x )/(8000C50 ) =1-0.5378 =0.4622

E(x)=nk/N =400*100/8000=50

2)as above

here defective batteries =60 ( please revert on this as information is confusing)

probability that you will receive 3 with defective radios =P(X=3) =0.0661

probability that you will receive 3.0 or more with defective batteries =P(X>=3) =1-P(X<=2)=0.9710

defective batteries will be observed in a sample of 200 =nk/N =20*60/200=6

3)P(X>=100) =0.0064

P(X<50)=0.0000148

E(x) =nk/N =400*1000/5000=80

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