Discuss the below:
Q1. The random variable x has a hypergeometric distribution, and the population contains 12 items. If you wanted to find the number of defects in a random sample of 3 selected items when the population contains 5 defects, identify the N, n, and r.
Q2. Using the following probability distribution table of the random variable x, what is the probability of x = 3? (Hint: All values of P(X) needs to sum to ?)
X P(X)
0 5/15
1 4/15
2 1/15
3 ?
Q3. The mean life of a pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months?