Identify whether the following is a description of a binomial or geometric distribution. Explain your reasoning.

a. The gender of the next 20 babies born at the local hospital is recorded. The random variable X represents the number of boys born. Would X have a binomial or geometric distribution?

b. You and your spouse have decided that you will continue to have children until you have a boy or have a maximum of 5 children. The random variable X represents the number of boys born. Would X have a binomial or geometric distribution?

c. Suppose that 28% of people who order fast food at a local fast food restaurant order a diet drink. You want to determine the how many people will order before someone orders a diet drink. The random variable X represents the number of people who order a diet drink at the local fast food restaurant. Would X have a binomial or geometric distribution?

d. It is estimated that 35% of people sleep a solid 6 hours each night. A researcher takes a sample of 20 people and X represents the number of people who sleep a solid 6 hours each night. Would X have a binomial or geometric distribution?

2. Suppose a company produces widgets and has a 20% defective rate.

a. What is the probability that 3 out of 10 randomly selected widgets are defective?

b. What is the probability that 6 or more out of the 10 randomly selected widgets are defective?

c. What is the probability that the first defective widget occurs on the fourth one selected?

3. Suppose that 16% of people in a population are left handed and we are randomly selecting 9 people from that group.

a. What is the probability the first left handed person is the 6th one selected?

b. What is the probability that exactly 4 of the 9 are left handed?

c. What is the probability that no more than 3 of the nine people are left handed?

4. Suppose that 7% of males are colorblind.

a. How many males will need to be tested before someone selected is colorblind?

b. What is the expected number of colorblind men in a group of 30?

c. What is the probability that none of the 30 men are colorblind?