Week 3 Assignment Introduction to Probability in Statistics
Question
There are eight players on a basketball team. They are practicing their free throws by having each player shoot two free throws. The table below shows the results of each player’s free throw attempts, where N represents a missed free throw and Y represents a made free throw. Construct the probability distribution of X for the number of free throws made by the players. Arrange x in increasing order and write the probabilities P(x) as simplified fractions.
| Player | Player 1 | Player 2 | Player 3 | Player 4 | Player 5 | Player 6 | Player 7 | Player 8 |
| Free Throws | NN | YY | NY | YN | YY | NY | NY | YY |
Question
For a certain animal, suppose that the number of babies born is independent for each pregnancy. This animal has a 70% chance of having 1 baby and a 30% chance of having 2 babies at each pregnancy. Let X be a random variable that represents the total number of babies if the animal gets pregnant twice. Construct a table showing the probability distribution of X. Arrange x in increasing order.
- Write the probabilities P(x) as decimals rounded to two decimals.
Answer:
Question
A poll was conducted to determine if there was any possible connection between men and women who live in a certain city and the favorability of a mayor in the city. In the poll, of the 400 men selected, 210 reported being in favor of the mayor. Of the 400 women selected, 190 also reported being in favor of the mayor. The probability of these results occurring by chance is calculated to be about 0.16. Interpret the results of the calculation at the 0.05 level of significance.
Question
A farmer claims that the average mass of an apple grown in his orchard is 100g. To test this claim, he measures the mass of 150 apples that are grown in his orchard and determines the average mass per apple to be 98g. The results are calculated to be statistically significant at the 0.01 level. What is the correct interpretation of this calculation?
Question
You bet $50 on 00 in a game of roulette. If the wheel spins 00, you have a net win of $1,750, otherwise you lose the $50. A standard roulette wheel has 38 slots numbered 00, 0, 1, 2, … , 36. What is the expected profit for one spin of the roulette wheel with this bet?
- Round your answer to the nearest cent.
- Enter an expected loss as a negative number.
Question
You toss a coin three times. If you toss heads exactly two times, you win $2. If you toss heads all three times, you win $8. Otherwise, you lose $3. What is the expected payout for one round of this game?
- Round your answer to the nearest cent.
- Enter an expected loss as a negative number.
Question
A standard roulette wheel with slots labeled 0, 00, 1, 2, 3, … , 36 is spun 60 times. Of these spins, the number 7 is spun 7 times. Assuming the wheel is fair, the probability of this occurring by chance is 0.00001. Do these results have statistical significance at the 0.01 level of significance?
Question
A hospital takes record of any birth that occurs there every day. On one day, the hospital reports that 35 of the 62 babies born were girls. Assuming that all of the parents did not have any gender selection procedures, there is a probability of 0.31 of getting these results by chance. Do these results have statistical significance at the 0.05 level of significance?
Question
Suppose you play a game where you toss three fair coins. If you get three tails, you win $10. Otherwise, you lose $2. If you were to play this game 15 times, how much would you expect to gain or lose?
- Do not round until the final answer.
- Enter an expected loss as a negative number.
Question
A flood insurance company sells policies for $700 per year. If a customer’s house is flooded, they are given $250,000 for repairs. The insurance company has calculated the chances that a house is flooded to be 1/2500 over the year. How much money can the insurance company expect to make with each policy sold?
- Round your answer to the nearest cent.
- Enter an expected loss as a negative number.
Question
In a day care center each child takes three classes and either passes or fails each class. The grades are shown in the table below. P represents a passed class, and F represents a failed class. Let X represent the number of classes failed by a child. Construct a probability distribution for X. Arrange x in increasing order and write the probabilities P(x) as simplified fractions.
| Child | Grades |
| Child 1 | PFP |
| Child 2 | PPF |
| Child 3 | FFP |
| Child 4 | PPP |
| Child 5 | PFP |
| Child 6 | PPF |
| Child 7 | FPF |
| Child 8 | PPP |
Question
For the probability distribution of X given below, find m.
- Enter m as a decimal rounded to one decimal place.
| x | 1 | 2 | 3 | 4 |
| P(x) | m | 2m | 3m | 4m |
Solution
Question
A poll was conducted to determine if there was any possible connection between men and women who live in a certain city and the favorability of a mayor in the city. In the poll, of the 400 men selected, 210 reported being in favor of the mayor. Of the 400 women selected, 190 also reported being in favor of the mayor. The probability of these results occurring by chance is calculated to be about 0.16. Interpret the results of the calculation at the 0.05 level of significance.
Answer: The difference in the proportions is not statistically significant because the probability is greater than 0.05.
Question
A farmer claims that the average mass of an apple grown in his orchard is 100g. To test this claim, he measures the mass of 150 apples that are grown in his orchard and determines the average mass per apple to be 98g. The results are calculated to be statistically significant at the 0.01 level. What is the correct interpretation of this calculation?
Answer: At the 0.01 level of significance,…………….please follow the link below to purchase the solution at $5
