Exam 12: Modeling Randomness

There are ten Academic Senate faculty in the Statistics Department at the University of California, Irvine: three females and seven males. Two faculty are to be selected without replacement to serve on a committee where one of those selected will serve as the head of the committee. -If we record the sex of the chosen committee members (male or female) and their roles (head or not), how many possible outcomes are in the sample space?

The volume in a can of soda is normally distributed with mean 358 mililiters (ml) and standard deviation 6 ml. -Fill in the blank: Approximately _____(1)_____ % of soda cans will be filled with less than 362 ml of soda.

Consider a random process that involves repeatedly rolling a rubber pig. If the pig lands on its feet, a person scores 10 points. Otherwise, a person scores zero points. Which of the following is a geometric random variable?

Suppose that 45% of customers at the local farmer's market prefer plastic bags to paper bags, whereas 62% of customers at the local grocery store prefer plastic bags to paper bags. You plan to take a simple random sample of 40 farmer's market customers and 40 grocery story customers and survey their bag preferences. Define p ̂_F-p ̂_G as the difference in sample proportions that prefer plastic bags to paper bags between the two locations (farmer's market - grocery store). -Calculate μ_(p_F-p_G ).

A tire manufacturer designed a new tread pattern for its all-weather tires. Repeated tests were conducted on cars of approximately the same weight traveling at 60 miles per hour. The tests showed that the new tread pattern enables the cars to stop completely in an average distance of 125 feet with a standard deviation of 6.5 feet and that the stopping distances are approximately normally distributed. -Now suppose you randomly select three cars from the study, and let X = the number of cars out of three randomly selected cars that will stop completely in a distance that is greater than 135 feet. What is the distribution of X?

In a large population of college students, 56% live in a campus residence hall, 62% participate in a campus meal program, and 42% do both. Define events R = student lives in a campus residence hall M = student participates in a campus meal program -Are the events and mutually exclusive?

Data on sex and opinion on the death penalty for respondents in the 2008 General Social Survey in which a random sample of 1,902 adults in the U.S. was surveyed are below. -What is the probability that the respondent is female and opposes the death penalty?

A soft drink company holds a contest in which a prize may be revealed on the inside of the bottle cap. The probability that each bottle cap reveals a prize is 0.39, and winning is independent from one bottle to the next. You buy six bottles. Let X be the number of prizes you win. -What is the standard deviation of the number of prizes in six bottles?

An online psychic (psi) ability or extrasensory perception (ESP) test shows the participant five face-down cards on the screen and asks the participant to "click on the one card that has a picture on the other side." After clicking a card, the test shows you the card to determine if your guess was correct. -How could you simulate one play of the game, assuming the participant did not have ESP abilities?