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Chapter 4: Q.30 (page 285)
P(x = 4) = _______
1
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Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 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.
What does the column 鈥�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.
A venture capitalist, willing to invest , has three investments to choose from. The first investment, a software company, has a chance of returning profit, a chance of returning profit, and a chance of losing the million dollars. The second company, a hardware company, has a chance of returning profit, a chance of returning profit, and a chance of losing the million dollars. The third company, a biotech firm, has a chance of returning profit, a of no profit or loss, and a chance of losing the million dollars.
a. Construct a PDF for each investment.
b. Find the expected value for each investment.
c. Which is the safest investment? Why do you think so?
d. Which is the riskiest investment? Why do you think so?
e. Which investment has the highest expected return, on average?
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.
The maternity ward at Dr. Jose Fabella Memorial Hospital in Manila in the Philippines is one of the busiest in the world with an average of 60 births per day. Let X = the number of births in an hour.
a. Find the mean and standard deviation of X.
b. Sketch a graph of the probability distribution of X.
c. What is the probability that the maternity ward will deliver three babies in one hour?
d. What is the probability that the maternity ward will deliver at most three babies in one hour?
e. What is the probability that the maternity ward will deliver more than five babies in one hour?
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