1. In New Mexico, 15% of residents are covered by Medicaid. 10%
of residents are covered by Medicare. 3% of residents are dual
eligible and covered by both Medicare and Medicaid. Draw a Venn
Diagram and then calculate the probability that a New Mexico
resident selected at random will be covered by either Medicare or
Medicaid.
2. A binomial distribution describes a random
variable, X, that has 4 possible outcomes. Outcome 1 has a
probability of 25%, Outcome 2 has a probability of 15%, Outcome 3
has a probability of 20%. What is the probability of Outcome 4?
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A salesperson makes four calls per year. A sample of 100 days given the following frequencies of sales volumes.
| Number of Sales | Observed Frequency (days) |
| 0 | 30 |
| 1 | 32 |
| 2 | 25 |
| 3 | 10 |
| 4 | 3 |
| TOTAL | 100 |
Records show sales are made to 30% of all sales calls. Assuming independent sales calls, the number of sales per day should follow a binomial distribution. The Binomial distribution is represented by:
For this exercise, assume that the population has a binomial probability distribution with n=4, p=0.30 and x= 0, 1, 2, 3 and 4.
(a) Compute the expected frequencies for x=0, 1, 2, 3 and 4 by using the binomial probability function. Combine categories if necessary to satisfy the requirement that the expected frequency is five or more for all categories.
(b) Use the goodness of fit test to determine whether the assumption of a binomial probability distribution should be rejected. Because no parameters of the Binomial probability distribution were estimated from the sample data, the degrees of freedom are k-1 .
