Question

1) If a fair die is rolled 25 times, what is the probability that a 3 is obtained exactly 3 times?

Round your answer to the nearest thousandth.

Use 1/6 as 0.167 in your calculations.

2) If X has a geometric distribution with parameter p = 0.523, calculate p(X=8)

Round your answer to the nearest thousandth.

3) The number of imperfections in an object has a Poisson distribution with a mean λ = 8.3. If the number of imperfections is 4 or less, the object is called “top quality.” If the number of imperfections is between 5 and 8 inclusive, the object is called “good quality.” If the number of imperfections is between 9 and 12 inclusive, the object is called “normal quality.” If the number of imperfections is 13 or more, the object is called “bad quality.” The number of imperfections in different objects are independent of each other.

A set of seven articles is taken. What is the probability that the set has exactly two top-quality, two good-quality, two normal-quality and one bad-quality objects?

Answer 1

Solution:-

1) The probability that a 3 is obtained exactly 3 times is 0.1929.

P(3) = 1/6 = 0.16666

n = 25

x = 3

By applying binomial distribution:-

P(x, n) = ⁿC_x*p^x*(1-p)^(n-x)

P(x = 3) = 0.1929