binomial distribution

explain why X DOES NOT have a binomial distribution: suppose a police office takes a two hour 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

we have a fixed period of time but not a fixed number of vehicles (observations). we do not have "n"

14. A recent survey in Michigan revealed that 60% of the vehicles traveling on highways, where speed limits are posted at 70 miles per hour, were exceeding the limit. Suppose you randomly record the speeds of ten vehicles traveling on US 131 where the speed limit is 70 miles per hour. Let X denote the number of vehicles that were exceeding the limit. Show X has a binomial distribution. Hint, what are the conditions that need to be met?

1. n=10 fixed number of observations (vehicles) 2. independent since random recordings 3. p =.60 chance of speeding overall 4. outcomes: speeding or not speeding

suppose 20% of all football fans get to attend a game in person. You sample 100 fans at random and want to find the probability that at least 15% of them get to attend a game in person. This problem represents a binomial distribution with n = 100. Which of these numbers represents the "p"?

20%

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 standard deviation of X is what?

4.33

The mean of a binomial probability distribution with n trials and probability p of success is: a. n + p b. np(1-p) c. np d. n + p - 1

c

Which of the following has a Binomial distribution? a. The number of people against a smoking ban out of a random sample of 100. b. The number of telephone calls received by a switchboard in a specified time period c. The number of customers arriving at a gas station on July 4 d. All of the above have a binomial distribution.

a

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.

b

explain why X DOES NOT have a binomial distribution: suppose 10% of OSU business students major in international marketing. you keep sampling students at random from our class until you find someone who is majoring in international marketing. let x = number of students you have to sample

we do not know n before the face and it would change everytime

explain why X DOES NOT have a binomial distribution: you have 10 different people working for you, 5 men and 5 women, and you have to choose different people to be on a committee that no one wants to be on. you put their names into a hat and pull out 3 names, one by one. let x = number of women who end up on the committee

the probability of picking woman starts out as 5/10, but once you pick out a person, there are only 9 left and the probability of choosing a woman changes. So, p is not the same every time.

explain why X DOES NOT have a binomial distribution: d. You take a random sample of 10 college students from stat 1430 and record their status (freshman, sophomore, etc.).

there are more than 2 possible outcomes each time: freshman, sophomore, junior, senior, etc