d. You take a random sample of 10 college students from stat 1430 and record their status (freshman, sophomore, etc.).
e. Suppose a police officer takes a two-hour time period and records the number of vehicles traveling on US 131 that exceed the speed limit (where the speed limit is 70 miles per hour). Let X denote the number of vehicles that were exceeding the limit. Explain why X does NOT have a binomial distribution.
4. Which of the following is not a characteristic of a binomial distribution?
a. There is a set of n trials
b. Each trial results in more than one possible outcome.
c. The trials are independent of each other.
d. Probability of success p is the same from one trial to another.
5. Which of the following has a Binomial distribution?
a. The number of customers arriving at a gas station on July 4
b. The number of people against a smoking ban out of a random sample of 100.
c. The number of telephone calls received by a switchboard in a specified time period
d. All of the above have a binomial distribution.
6. The standard deviation of a binomial probability distribution with n trials and probability p of success is:
a. np
b. square root of (np(1-p))
c. n + p
d. np(1-p)
7. One out of four of the students in an English class is an international student. Take a random sample of 100 students from this class and let X = the number of international students. The mean of X is what? (Note! You are not given p directly but you can find it):
a. 18.75
b. 4.33
c. 25
d. 5
8. If 30% of Americans own a pet and you select 100 Americans at random and let X = the number who own a pet. What is the mean and standard deviation of X?
For the following problems show your work, and make sure you use probability notation in your work. For example, if trying to find the probability that X is greater than 2 write: P(X>2).
9. 30% of OSU students have cars that are black. Suppose you randomly sample 5 OSU students, and let X be the number of students in the sample with black cars. Find the probabilities of the following events.
a. Exactly 3 students in the sample have black cars.
b. More than 3 students in the sample have black cars.
c. Less than half of the students in the sample have black cars.