Statistical Terminology and Theoretical Probability Analysis 1 Assignment 4
NOTE: Show your work in the problems.
- In families with four children, you’re interested in the probabilities for the different possible numbers of girls in a family.
- Using theoretical probability (assume girls and boys are equally likely), compile a five-column table with the headings “0” through “4,” for the five possible numbers of girl children in a four-child family. Then, using “G” for girls and “B” for boys, list under each heading the various birth-order ways of achieving that number of girls in a family.
Statistical Terminology and Theoretical Probability
Then, use your table to calculate the following probabilities:
- The probability of 1 girl
- The probability of 2 girls
- The probability of 4 girls
- The probability the third child born is a girl
- As pictured in Figure 6.11 of your textbook, a roulette wheel has 38 numbers: 18 odd black numbers from 1 to 35, 18 even red numbers from 2 to 36, and the two green numbers 0 and 00. Using theoretical probability, calculate the following:
- The probability of spinning a green number
- The probability of spinning a number greater than 30
- The probability of spinning a red number less than 10
- The probability of spinning an even black number
- The expected total of green numbers in 57,000 spins
- In a nationwide polls of 1,500 randomly selected U.S. residents, 77% said that they liked pizza. In a poll of 1,500 randomly selected U.S. residents one month later, 75% responded that they liked pizza.
- Does the polling evidence support the claim that pizza declined in popularity over the month between polls? Explain why or why not.
- Using statistical terminology, precisely identify the population parameter the two polls were attempting to measure. How does a parameter differ from a statistic?
Statistical Terminology and Theoretical Probability
- Based on the two polls, what would you say to someone who guessed that the population parameter the polls are trying to measure is really only 50%?
- Eleven people have eleven different favorite numbers from 2 to 12. They all agree to participate in a 10,000-roll dice
game where they bet $1 on their favorite number for each roll of two standard (fair) dice. A donor kicks in an extra dollar every round, so the payoff if your number comes up is $12.
- Assuming everyone bets on all 10,000 rounds, what is the expected value for a person who has number 7? (Show your calculations.)
- Assuming everyone bets on all 10,000 rounds, what is the expected value for a person who has number 2? (Show your calculations.)
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