A manufacturing machine has a 5% defect rate.If 8 items are chosen at random, what is the probability that at least one will have a defect?

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?

Assume that when adults with smartphones are randomly​ selected,44​%use them in meetings or classes. If7adult smartphone users are randomly​ selected, find the probability that exactly3of them use their smartphones in meetings or classes.

The p-value.
Given: The size of the sample (n) is 15.

In a recent​ poll, 45​% of survey respondents said​ that, if they only had one​ child, they would prefer the child to be a boy. Suppose you conducted a survey of 160 randomly selected students on your campus and find that 79 of them would prefer a boy. Complete parts​ (a) and​ (b) below.
Click here to view the standard normal distribution table (page 1).
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Click here to view the standard normal distribution table (page 2).
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​ (a) Use the normal approximation to the binomial to approximate the probability​ that, in a random sample of 160 ​students, at least 79 would prefer a​ boy, assuming the true percentage is 45​%.
The probability that at least 79 students would prefer a boy is 3636.
​ (Round to four decimal places as​ needed.)

An oil company conducts a geologival survey that indicates an exploratory oil well should have a 23% change of striking oil.
A. What is the probability that the 2nd strike will occur on the 5th attempt?
B. What is the probability that the 7th strike will occur on the 12th attempt?
C. What is the probability that the 11th strike will occur between the 15th and 18th attempt?

What is the mean of the binomial distribution for which ${\displaystyle n=20\text{and}p=0.2}$?

Consider Bernoulli trials with success probability ${\displaystyle p=\frac{1}{4}}$. What is the probability that the first success occurs in the fourth trial?