Question

Are the following random variables binomial? If it is, state the possible values of the random variable. If not, state why. (Hint: Check the five characteristics of a binomial experiment that we discussed in class.)

(a) Bob is teaching his daughter Tina to drive. They have one driving lesson a day for one week. X = the number of days that Tina successfully goes without hitting another car.

(b) Joey and Chandler are playing a board game that involves rolling a pair of dice. The first person to roll doubles in this game gets ten extra points, and Joey is intent on winning. Let Y = the number of rolls until he gets doubles.

(c) El Taco Loco, a local Mexican restaurant, has a challenge on their menu: If you can eat ten tacos within a 2-hour period, your meal is free. Only 3% of people typically complete the challenge. One weekend, the restaurant staff watch 100 customers attempt to eat this massive meal. Let N = the number of customers who complete the challenge.

(d) Dwight tries to impress Angela with a card trick that involves randomly drawing 7 cards from a standard 52-card deck without replacement. (Angela is unimpressed by this.) Let Z = the number of hearts she draws

Answer 1

binomial experiment is a statistical experiment that has the following properties:

• The experiment consists of n repeated trials.
• Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure.
• The probability of success, denoted by P, is the same on every trial.
• The trials are independent; that is, the outcome on one trial does not affect the outcome on other trials.

Hence in first example either she hits a car or doesn't. So only two independent outcomes are there. So it is a binomial distribution.

In 2nd one there are not only two outcomes results may outcomes would be present. So it is not a binomial distribution.

In 3rd one there are only two outcomes either they can eat or can't. But in this case outcome of first trial influence the other that is eating ten tacos. So it is not a binomial distribution.

In 4th case there are so many tricks that can be done with 7 cards which are randomly choosen. But this influence the other event which is impression to be grabbed. So it is not a binomial distribution.