Question

1.) For each of the following, determine whether the random variable described is binomial. If it is binomial, state its parameters and possible values. If it is not binomial, state why.

(a) You are playing a board game that involves spinning a wheel with five different colors. The first person whose spinner lands on the orange section (p = 0.2) gets the advantage of going first. Let X = the number of spins until you land on orange

(b) While playing poker, you draw five cards from a deck without replacement. Let Y = the number of aces you draw.

(c) According to data collected by the National Parks Service, a certain park reports that you have a 34% chance of seeing a bear while on a hike. You interview 30 solo hikers and ask them if they saw a bear. let B = the number of hikers who see a bear

2.) You browse a menu that has 16 possible appetizers to choose from. You and your friends want to order the sampler platter, which allows you to choose from three appetizers. How many possible combinations of appetizers are there? (Hint: use the binomial coefficient)

3.) Clarinex-D is a medication whose purpose is to reduce the symptoms associated with a variety of allergies. In clinical trials of Clarinex-D, 5% of patients in the study experience insomnia as a side effect. A random sample of 25 Clarinex-D users id obtained, and the number of patients X who experience insomnia recorded.

(a) Find the probability that exactly 3 patients experience insomnia as a side effect.

(b) Find the probability that 2 or fewer experience insomnia as a side effect.

Answer 1