# Question: determine the most appropriate distribution that will best describe the...

###### Question details

Determine the most appropriate distribution that will best describe the given random variable. Clearly state the appropriate probability density function and the value of the relevant parame- ter(s).

a. Andrew would like to observe the behavior of customers in a coffee shop. His- torically, an average of 5 customers order a “tall iced cafe mocha” per thirty minute interval. He would like to determine X, the number of customers who will order a “tall iced cafe mocha” in the next 30 minutes.

b. Nate is inspecting a box of 100 light bulbs. From past data, exactly 10 bulbs in every box of 100 light bulbs will have a lifetime of less than 200 hours. He is interested in checking this assumption. To do so, he will obtain the amount of time that a light bulb will be in use before it dies out. Thus, any light bulb chosen will not be returned to the box. He will take a random sample of 10 light bulbs and will observe Y , the number of light bulbs that will have a lifetime of less than 200 hours.

c. Jack was absent from class for the past three weeks. He came back the day of a test. This test consists of 100 problems where each problem has 4 choices. Since he has absolutely no idea on the coverage of the test, he will merely guess an answer to each problem. This means that his answer to one problem is independent of his answer to another problem. Let W be the number of correct answers that he will get on the test.