Identifying N P and x 1 For each situation identify the sam

(Identifying N, P, and x ) 1. For each situation, identify the sample size n, the probability of success p, and the number of successes x. Give the answer in the form b(n,p,x). Do not go on to find the probability. Assume the four conditions for a binomial experiment are satisfied.

a. In the 2008 presidential election, 54% of the voters voted for president Obama. What is the probability that 65 out of 100 independently chosen voters voted for president Obama?

b. The manufacturer of LoJack stolen Vehicle Recovery System claims that the probability that a stolen vehicle using Lojack will be recovered is 90%. What is the probability that exactly 9 out of 10 independently stolen vehicles with Lojack will be recovered?

c. A student is taking a 10-question multiple-choice test. Each question has four options:a,b,c, and d. One of these four options is correct and three of them are incorrect. What is the probability that the student correctly answers exactly 6 of the 10 questions on the test by guessing?

Solution

a. In the 2008 presidential election, 54% of the voters voted for president Obama. What is the probability that 65 out of 100 independently chosen voters voted for president Obama?

N = 100
P = 0.54
x = 65

b. The manufacturer of LoJack stolen Vehicle Recovery System claims that the probability that a stolen vehicle using Lojack will be recovered is 90%. What is the probability that exactly 9 out of 10 independently stolen vehicles with Lojack will be recovered?

N = 10
P = 0.90
x = 9

c. A student is taking a 10-question multiple-choice test. Each question has four options:a,b,c, and d. One of these four options is correct and three of them are incorrect. What is the probability that the student correctly answers exactly 6 of the 10 questions on the test by guessing?

N = 10
P = 0.25
x = 6