Consider a binominal experiment with 2 trials and p=0.4 a. Compute

At a certain college, 6% of all students come from outside the United States. Incoming students there are assigned at random to freshman dorms, where students live in residential clusters of 40 freshmen sharing a common lounge area. How many international students would you expect to find in a typical cluster? With what standard deviation?

Let X be a binomial random variable with ${\displaystyle p=0.3}$ and ${\displaystyle n=15}$
What is ${\displaystyle P(X=5)}$?

When Julia is writing a first draft, there is 0.7 probability that there will be no spellin mistakes on a page.
One day, Julia writes a first draft that is 4 pages long.
Assuming that Julia is equally likely to have a spelling mistake on each of the 4 pages, what is the probability that she will have no spelling mistakes on at least one of them?
Round your answer to the nearest hundredth.

Find the right choice “Continuity correction is used when the using the … to …” a) normal approximation, binomial probability b) binomial probability, normal approximation c) binomial approximation, normal probability d) normal probability, binomial approximation

A company prices its tornado insurance using the following assumptions:• In any calendar year, there can be at most one tornado.• In any calendar year, the probability of a tornado is 0.09.• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 21-year period.

If you play roulettes and bet on red the probability that you win is ${\displaystyle \frac{18}{38}=.4737}$. People often repeat this between several times. We can consider each time we play a trial and consider it a success when we win, so ${\displaystyle p=\frac{18}{38}\text{or}\left(.4737\right)\text{and}q=\frac{20}{38}}$ or (.5263).
Suppose that Caryl always places the same bet when she plays roulette, $5 on red. Caryl might play just once, or might play several times. She has a profit (having won $5 more times than she lost $5) if she wins more than half of the games she plays.
a) what is the probability that Caryl has a profit if she plays only one time?
b) suppose Caryl has decided that she is going to play 13 times. to find the probability that has a profit, we can treat this like a binomial. Show the calculator input and result as your calculator to find the probability that she makes a profit when she plays 13 times.

A coin is tossed 16 times. What is the probability of obtaining exactly 14 heads?