X takes on the values 0, 1, 2, 3, …, A fair, six-sided die is rolled ten times. Each roll is independent. You want to find the probability of rolling a one more than three times. Each student does homework independently. In a statistics class of 50 students, what is the probability that at least 40 will do their homework on time? Students are selected randomly. If we are interested in the number of students who do their homework on time, then how do we define X?
Give two reasons why this is a binomial problem. If 20 adult workers are randomly selected, find the probability that at most 12 of them have a high school diploma but do not pursue any further education. How many adult workers do you expect to have a high school diploma but do not pursue any further education? Enter 20,0. The probability that at most 12 workers have a high school diploma but do not pursue any further education is 0. If 30 students are selected at random, find the probability that at most 14 of them participate in a community volunteer program outside of school.
Eight of the pages feature signature artists. Suppose we randomly sample pages. The lifetime risk of developing pancreatic cancer is about one in 78 1. Suppose we randomly sample people.
DeAndre scored with Suppose you choose a random sample of 80 shots made by DeAndre during the season. The following example illustrates a problem that is not binomial.
It violates the condition of independence. ABC College has a student advisory committee made up of ten staff members and six students. The committee wishes to choose a chairperson and a recorder. What is the probability that the chairperson and recorder are both students? The names of all committee members are put into a box, and two names are drawn without replacement. The first name drawn determines the chairperson and the second name the recorder. There are two trials. However, the trials are not independent because the outcome of the first trial affects the outcome of the second trial.
The probability of a student on the first draw is. The probability of a student on the second draw is , when the first draw selects a student. The probability is , when the first draw selects a staff member. A lacrosse team is selecting a captain. The names of all the seniors are put into a hat, and the first three that are drawn will be the captains. The names are not replaced once they are drawn one person cannot be two captains.
You want to see if the captains all play the same position. State whether this is binomial or not and state why. Newport, Frank. Pryor, John H. A statistical experiment can be classified as a binomial experiment if the following conditions are met:. Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from , incoming first-time, full-time freshmen from four-year colleges and universities in the U.
Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status.
According to a recent article the average number of babies born with significant hearing loss deafness is approximately two per 1, babies in a healthy baby nursery. The number climbs to an average of 30 per 1, babies in an intensive care nursery. Suppose that 1, babies from healthy baby nurseries were randomly surveyed. Find the probability that exactly two babies were born deaf. Use the following information to answer the next four exercises. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu.
Find the probability that at least four of the 25 patients actually have the flu. On average, for every 25 patients calling in, how many do you expect to have the flu? People visiting video rental stores often rent more than one DVD at a time. There is five-video limit per customer at this store, so nobody ever rents more than five DVDs.
A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet Vietnamese New Year festivities this year. We are interested in the number of students who will attend the festivities. Use the following information to answer the next two exercises: The probability that the San Jose Sharks will win any given game is 0. An upcoming monthly schedule contains 12 games.
For example,. An example will make clear the relationship between random variables and probability distributions. Suppose you flip a coin two times. Now, let the variable X represent the number of Heads that result from this experiment. The variable X can take on the values 0, 1, or 2. In this example, X is a random variable; because its value is determined by the outcome of a statistical experiment. Consider the coin flip experiment described above. The table below, which associates each outcome with its probability, is an example of a probability distribution.
A cumulative probability refers to the probability that the value of a random variable falls within a specified range.
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We and our partners process data to: Actively scan device characteristics for identification. I Accept Show Purposes. Your Money. Personal Finance. Your Practice. Popular Courses. Financial Analysis How to Value a Company. What Is a Probability Distribution? Key Takeaways A probability distribution depicts the expected outcomes of possible values for a given data generating process. Probability distributions come in many shapes with different characteristics, as defined by the mean, standard deviation, skewness, and kurtosis.
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