## Question

In an experiment of rolling 10 dice simultaneously. Use the binomial distribution to calculate the followings:

b) The probability of getting six, seven, or eight 3’s

Question 2

In a bag of 25 marbles, the probability of any one marble being cracked is 0.2

a) Use the Binomial approximation to calculate the probability that at least three marbles are cracked?

b) Use the Poisson approximation to calculate the probability that at least three marbles are cracked?

c) Compare the results of parts a and b, then illustrate on how well the Poisson probability distribution approximates the Binomial probability distribution.

Question 3

In an order of 400 milk cartons, there are 15 spoiled ones. A quality inspector randomly collects 10 cartons for inspection to determine whether they are defective. Use the Hypergeometric approximation to calculate the probability that there are at most 5 spoiled ones in the inspectors’ sample batch, P(X<=5).

## Solution Preview

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Question 1In an experiment of rolling 10 dice simultaneously. Use the binomial distribution to calculate the followings:

b) The probability of getting six, seven, or eight 3’s

Since probability of getting 3’s from the dice p =1/6

We are rolling dice 10 time. Using binomial distribution, taking n =10, r =6, 7 and 8 , p = 1/6

P(x = 6) + P(x = 7) + P(x = 8)...

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