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Use the following information to answer the next six 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 select freshman from the study until you find one who replies 鈥測es.鈥� You are interested in the number of freshmen you must ask.

What values does the random variable X take on?

Use the following information to answer the next six 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 select freshman from the study until you find one who replies 鈥測es.鈥� You are interested in the number of freshmen you must ask.

Construct the probability distribution function (PDF). Stop at x = 6.

On May 11, 2013 at 9:30 PM, the probability that moderate seismic activity (one moderate earthquake) would occur in the next $48$hours in Japan was about $1.08\%$. As in Example $4.8$, you bet that a moderate earthquake will occur in Japan during this period. If you win the bet, you win $\backslash (100$. If you lose the bet, you pay$\backslash )10$. Let X = the amount of profit from a bet. Find the mean and standard deviation of X.

Use the following information to answer the next six 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 select freshman from the study until you find one who replies 鈥測es.鈥� You are interested in the number of freshmen you must ask.

On average (渭), how many freshmen would you expect to have to ask until you found one who replies "yes?"

The state health board is concerned about the amount of fruit available in school lunches. Forty-eight percent of schools in the state offer fruit in their lunches every day. This implies that 52% do not. What would a "success" be in this case?

What does the column 鈥�$P\left(x\right)$鈥� sum to?

Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to

sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established

a probability distribution.

Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are $16$business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.

$X~\_\_\_\_\_(\_\_\_\_\_,\_\_\_\_\_)$

Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are $16$business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.

What values does $X$take on?

Use the following information to answer the next six exercises: On average, a clothing store gets $120$customers per day.

Assume the event occurs independently in any given day. Define the random variable $X$.

Define the random variable $X$.