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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. State the probability question mathematically.

Sixty-five percent of people pass the state driver’s exam on the first try. A group of $50$individuals who have taken the driver’s exam is randomly selected. Give two reasons why this is a binomial problem.

About $32\%$ of students participate in a community volunteer program outside of school. 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. Use the $TI-83+orTI-84$ calculator to find the answer.

According to a Gallup poll, 60% of American adults prefer saving over spending. Let X = the number of American adults out of a random sample of 50 who prefer saving to spending.

a. What is the probability distribution for X?

b. Use your calculator to find the following probabilities:

i. the probability that 25 adults in the sample prefer saving over spending

ii. the probability that at most 20 adults prefer saving

iii. the probability that more than 30 adults prefer saving

c. Using the formulas, calculate the

(i) mean and

(ii) standard deviation of X.

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.

Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from $203,967$incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. $71.3\%$ of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. 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.

What is the standard deviation$\left(\mathrm{σ}\right)$?

Jeremiah has basketball practice two days a week. Ninety percent of the time, he attends both practices. Eight percent of the time, he attends one practice. Two percent of the time, he does not attend either practice. What is X and what values does it take on?

The probability of a defective steel rod is $0.01.$ Steel rods are selected at random. Find the probability that the first defect occurs on the ninth steel rod. Use the $TI-83+orTI-84$ calculator to find the answer.

The literacy rate for a nation measures the proportion of people age 15 and over who can read and write. The literacy rate for women in Afghanistan is 12%. Let X = the number of Afghani women you ask until one says that she is literate.

a. What is the probability distribution of X?

b. What is the probability that you ask five women before one says she is literate?

c. What is the probability that you must ask ten women?

d. Find the (i) mean and (ii) standard deviation of X.

A gross of eggs contains 144 eggs. A particular gross is known to have 12 cracked eggs. An inspector randomly chooses 15 for inspection. She wants to know the probability that, among the 15, at most three are cracked. What is X, and what values does it take on?