A) Assume that 12 jurors are randomly selected from a population in which 87% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities.

Find the probability of exactly 5 Mexican-Americans among 12 jurors.
P(x=5)=P(x=5)=

Find the probability of 5 or fewer Mexican-Americans among 12 jurors.
P(x≤5)=P(x≤5)=

Does 5 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?

yes?

no?

B) A company prices its tornado insurance using the following assumptions:
• In any calendar year, there can be at most one tornado.
• In any calendar year, the probability of a tornado is 0.12.
• The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year.
Using the company's assumptions, calculate the probability that there are fewer than 4 tornadoes in a 14-year period.

1. T F The number of defects on a product produced by a process is distributed as a Poisson distribution.

2. T F For large binomially distributed populations and small samples you can use sampling without replacement

3. T F Given a triangular distribution with minimum 2, maximum 8 and mode 7, the probability of being smaller than 7 is greater than 60%

4. T F The hypergeometric distribution describes sampling without replacement

5. T F The relative frequency of a value is the proportion of times the value occurs.

6. T F The permutation of n numbers is always smaller than the combination of the same n numbers, taken the same number of times

7. T F The intersection of two events is greater than zero when they are mutually exclusive

8. T F The probability of rolling a 6 with a fair six sided die is 1/6.

9. T F The product of the probability of two independent events is called conditional probability.

10. T F When we use both a beta and a triangular distribution to represent a variable, the probability of a low value will always be grater with the triangular distribution

QUESTION 4 ( 8 marks)

A telemarketer is able make a sale on 27% of the phone calls he makes. Assume that he makes 12 calls in an hour. Answer the following questions, assuming a binomial probability distribution:

Required:

1. What is the probability that he will make exactly four sales in the course of an hour? ( 3 marks)
2. What is the probability that he will make at least three sales in the course of an hour? Hint: Use the approach that requires the least calculation work! ( 5 marks)

Suppose 1.6% of the antennas on new Nokia cell phones are defective. For a random sample of 235 antennas, answer the following questions (assume a Poisson probability distribution):

Required:

1. Calculate the mean and standard deviation for the probability distribution of the number of defective antennas in the random sample. ( 2 marks)
2. What is the probability that exactly five of the antennas will be defective? What is the probability that less than three antennas will be defective? ( 4 marks)

i need fully explanation and calculation of the answer

QUESTION 4 ( 8 marks)

A telemarketer is able make a sale on 28% of the phone calls he makes. Assume that he makes 11 calls in an hour. Answer the following questions, assuming a binomial probability distribution:

Required:

1. What is the probability that he will make exactly four sales in the course of an hour? ( 3 marks)

2. What is the probability that he will make at least three sales in the course of an hour? Hint: Use the approach that requires the least calculation work! ( 5 marks)

QUESTION 5 ( 8 marks)

Suppose 1.5% of the antennas on new Nokia cell phones are defective. For a random sample of 240 antennas, answer the following questions (assume a Poisson probability distribution):

Required:

1. Calculate the mean and standard deviation for the probability distribution of the number of defective antennas in the random sample. and What is the probability that exactly five of the antennas will be defective? ( 4 marks)
2. What is the probability that less than three antennas will be defective? ( 4 marks)

The number of customers arriving per hour at a certain automobile service facility is assumed to follow a Poisson distribution with mean λ=5.

a) Compute the probability that more than 11 customers will arrive in a 2​-hour period.

b) What is the mean number of arrivals during a 2​-hour ​period?

The number of M&M's in a package normally distributed with a mean of 48 candies and a standard deviation of 3. Lets say that we get 40 packages of M&M's. What is the probability that the average number of candies in those 40 packages is between 46 and 49?

0.49999

0.9825

0.3781

0.96499

The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the average number of passing yards per attempt (Yards/Attempt) and the percentage of games won (WinPct) for a random sample of 10 NFL teams for the 2011 season.†

A. Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt. (Round your numerical values to three decimal places.)

B. For the 2011 season, suppose the average number of passing yards per attempt for a certain NFL team was 6.4. Use the estimated regression equation developed in part (c) to predict the percentage of games won by that NFL team. (Note: For the 2011 season, suppose this NFL team's record was 8 wins and 8 losses. Round your answer to the nearest integer.)

The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the average number of passing yards per attempt (Yards/Attempt) and the percentage of games won (WinPct) for a random sample of 10 NFL teams for the 2011 season.†

(c)

Develop the estimated regression equation that could be used to predict the percentage of games won given the average number of passing yards per attempt. (Round your numerical values to three decimal places.)

ŷ =

e)

For the 2011 season, suppose the average number of passing yards per attempt for a certain NFL team was 6.1. Use the estimated regression equation developed in part (c) to predict the percentage of games won by that NFL team. (Note: For the 2011 season, suppose this NFL team's record was 7 wins and 9 losses. Round your answer to the nearest integer.)

  %

Using the previous tutorial, address the following: Imagine an experiment where three dice are tossed and the numbers on each die is recorded under Die1, Die2 and Die3. Answer the following questions about the sum of the three numbers recorded from: Die1+Die2+Die3. (Discussions allowed)

Hint:

Simulate this experiment 1000 times. (use the same procedure as in the above tutorial, but for the Number of Variables, instead of 1 put 3; since we are rolling 3 dice not one).
Next, create a new column by writing, in cell D1 =A1+B1+C1, and scroll down the results by clicking on D1 cell and bottom-right corner. (for more detail see the Book chapter on lecture 26)
Finally create the histogram based on this new column. Use bins 3,4,5,…,18.
16. What is the (approximate) probability that Die1+Die2+Die3=8?

a. Probability is approximately 5%
b. Probability is approximately 10%
c. Probability is approximately 20%
d. Probability is approximately 25%
17. What is the (approximate) probability that Die1+Die2+Die3<7?

a. Probability is approximately 5%
b. Probability is approximately 10%
c. Probability is approximately 15%
d. Probability is approximately 20%
18. What is the (approximate) probability that Max(Die1,Die2,Die3)=5? Careful: Use “Max( ) function in Excel.

a. Probability is approximately 5%
b. Probability is approximately 15%
c. Probability is approximately 25%
d. Probability is approximately 45%