answer quickly and correctly for full reward 1 The number o

answer quickly and correctly for full reward !

1. The number of kittens in a litter is an example of a discrete random variable. A) True B) False 2. The mean number of customers arriving at a bank during a 15-minute period is 10. Find the probability that exactly 8 customers will arrive at the bank during a 15-minute period. A) 0.0194 B) 0.0003 C) 0.1126 D) 0.0390 3. Forty-three percent of marriages end in divorce. You randomly select 15 married couples. Find the probability exactly 5 of the marriages will end in divorce. A) 0.333 B) 0.039 C) 0. 160 D) 0.015 4. Determine the probability distribution?s missing probability value. A) 0. 15 B)0.25 C) 0.35 D) 0.65 5. A fair die is rolled until a 2 appears. Find the probability that the first 2 appears on the fifth roll of the die. A) 0.482 B) 0.067 C) 0.0006 D) 0.080

Solution

(1) True

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(2) Given X~Poisson(mean=10)

P(X=x)=(10^x)*exp(-10)/x!

So the probability is

P(X=8) =(10^8)*exp(-10)/8! =0.112599

Answer: C

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(3)Given X follows Binomial distribution with n=15, p=0.43

P(X=x)=15Cx*(0.43^x)*(1-0.43)^(15-x)

So P(X=5) =15C5*(0.43^5)*(1-0.43)^(15-5) =0.1598255

Answer: C

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(4)1-0.25-0.3-0.1 =0.35

Answer: C

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(5) (5/6)^4*(1/6) =0.08037551

Answer: D