Hypergeometric distribution and normally distribution

1. The random variablex has a hypergeometric distribution, and the population contains 12 items. If you wanted to find the number of defects in a random sampleof 3 selected items when the population contains 5 defects, identify the N, n, and r.

2. Using the following probabilitydistribution 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 ?

3. The meanlife of a pair of shoes is 40 months with a standard deviationof 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?

Answer:

1. Since the population contains 12 items, N=12
Since the population contains 5 defects, r=5
Since we …

The solution gives detailed steps on solving 3 questions regarding the hypergeometric distribution and normally distribution. Probability distribution table is used to determined the probability when x=3.