Notation
what is the number of trials
What is the expected value of a Binomial random variable?
What is np?
Assume in a large population, 27% of people own at least one cat. You would like to survey a random sample from this population, but would like to make sure you have at least 20 cat-owners in your sample. You randomly select people from the population to take your survey until 20 cat-owners have taken the survey. Let X = the total number of people surveyed. X is not a binomial random variable because which condition is violated?
What is fixed number of trials?
There are a dozen puppies in a kennel. 3 are corgis and the rest are dalmations. If you reach in 20 times (replacing the dog after every round), what’s the probability of grabbing a corgi 7 times?
What is 0.112?
dbinom(7, 20, 3/12)
BINOM.DIST(7, 20, 3/12)
What is the notation for success ?
what is p?
What is the standard deviation of a Binomial random variable?
What is sqrt(np(1-p))?
There are ten Academic Senate faculty in the CSUEB Statistics Department, five females and five males. Two faculty are to be selected without replacement to serve on a committee and the gender of each will be recorded. Let X = the number of female faculty on the committee. Which condition is not satisfied?
What is probability of success stays the same?
There are 5 new disney live-action remakes. The probability that they will be mind numbingly bad is 89%. What’s the probability that less than 3 are genuinely enjoyable?
What is 0.989
pbinom(2, 5, 0.11)
BINOM.DIST(2, 5, 0.11, TRUE)
In a binomial distribution, what are the two parameters that determine the shape of the distribution?
What is n and p?
The probability is p = 0.80 that a patient with a certain disease will be successfully treated with a new medical treatment. Suppose that the treatment is used on 40 patients. What are the possible values of X = number of patients that were successfully treated?
What is 0, 1, 2, ..., 40?
A binomial distributed random variable has ___ possible outcomes: ______ or ______?
What is 2, success or failure?
Tom is trying to catch Jerry using a mouse trap. Jerry is good at avoiding them, so the chances of him being caught are 0.1%. Tom tried to use this trap everyday for a week. What are the chances that Jerry doesn’t get caught at all during the week?
what is 0.993?
dbinom(0, 7, 0.001)
BINOM.DIST(0, 7, 0.001)
Suppose 23% of all CSUEB students own a car. We take a simple random sample of three CSUEB students. We are interested in the probability that at least one of the three selected students owns a car. Write the probability statement.
What is P(X >= 1)?
Poll time! Taylor or Beyonce? Raise your hand if you vote "Beyonce". Suppose we randomly select 5 students in our class.
Let X = number of students out of 5 who vote for Beyonce over Taylor.
Calculate the probability that none of the students vote Beyonce over Taylor, P(X = 0).
P(X = 0) = p^0 * (1 - p)^5
In a large restaurant 3/5 customers ask for water with their meal. A random sample of 10 customers is selected. Is X = the number of customers out of 10 that ask for water a Binomial random variable? (Be prepared to explain).
What is yes?
You’re playing Russian Roulette with 1 covid shot and 5 shots of poison. If the shots are refilled after every round, and there are 10 rounds, what’s the probability of getting the covid shot 4 or more times?
What is 0.0697.
** 1-Binomcdf (10, ⅙, 3)
About one-third of all adults in the United States have type O+ blood. Suppose three randomly selected adults donate blood. Define the random variable X = the number of the three randomly selected adults that have type O+ blood. X ~ ?
What is X ~ Binom(n = 3, p = 1/3)?
Consider a random circumstance that involves repeatedly rolling a rubber pig. If the pig lands on its feet, a person scores 10 points. Otherwise, a person scores zero points. Which of the following is a binomial random variable?
a. The number of times the pig lands on its feet when the pig is rolled 20 times.
b. The number of rolls until the pig lands on its feet for the first time.
c. The total number of points a person scores in five tosses.
d. The time the pig spends in the air on one roll.
What is a?
Suppose 23% of all CSUEB students own a car. We take a simple random sample of three CSUEB students. What is the probability that no more than three of the selected students owns a car?
What is 1?