The number of hours spent per week on household chores by all adults has a mean of 28.6 hours and a standard deviation of 8.8 hours. The probability, rounded to four decimal places, that the mean number of hours spent per week on household chores by a sample of 64 adults will be more than 26.75 is:

A coin that lands on heads with a probability of p is tossed multiple times. Each toss is independent. X is the number of heads in the first m tosses and Y is the number of heads in the first n tosses. m and n are fixed integers where 0 < m < n. Find the joint distribution of X and Y.

random experiment was conducted where a Person A tossed five coins and recorded the number of “heads”. Person B rolled two dice and recorded the average the two numbers. Simulate this scenario (use 10000 long columns) and answer questions 10 to 13.

Hint: check Lectures 26 and 27 in the Book.

10. Which of the two persons (A or B) is more likely to get the number 5?

a. Person A

b. Person B

c. Not possible to determine

11. Which of the two persons will have higher Median among their outcomes?

a. Person A

b. Person B

c. Not possible to determine

12. What is the probability that person B obtains number 5 or 6?

a. About 10%

b. About 20%

c. About 30%

c. About 55%

13. Which of the persons has higher probability of getting the number 3 or larger?

a. Person A

b. Person B

c. Not possible to determine

A random experiment was conducted where a Person A tossed five coins and recorded the number of “heads”. Person B rolled two dice and recorded the sum the two numbers. Simulate this scenario (use 10000 long columns) and answer questions 10 to 13.

Hint: check Lectures 26 and 27 in the Book.

10. Which of the two persons (A or B) is more likely to get the number 4?

• a. Person A
• b. Person B
• c. Not possible to determine

11. Which of the two persons will have higher Median among their outcomes?

• a. Person A
• b. Person B
• c. Not possible to determine

12. What is the probability that person B obtains number 5 or 6?

• a. About 15%
• b. About 25%
• c. About 35%
• c. About 55%

13. Which of the persons has higher probability of getting the number 3 or smaller?

• a. Person A
• b. Person B
• c. Not possible to determine

Problem 1) W congested computer network has a 2% chance of losing a data packet (lost packets must be resent), and a packet losses are independent events. An e-mail message requires 100 packages.

(1) what is the distribution of the number of data packets that must be resent? Please choose one below.

(A) Binomial (B) Geometric (C) Poisson

(2) What is the probability that at least one packet must be resent?

(3) What is the mean of the number of packets that must be resent?

(4) What is the standard deviation of the number of packets that must be resent?

Problem 2) From 500 customers, a major appliance manufacturer randomly selects 5 customers without replacements. The company estimates that 125 of the customers will reply to the survey.

(1) What are the possible values that X takes where X = the number in the same reply tot he survey?

(2) What is the probability that at most one customers in the sample reply tot he survey?

An exhaustive study of all active Facebook accounts was recently conducted by Facebook. One variable Facebook recorded was the number of friends X of each Facebook user. Suppose X has expected value E(X) = 180 and standard deviation SD(X) = 280.7. Since the possible values of X are only integers and since the distribution of X is highly skewed to the right, the distribution of X cannot be described by a normal model. Suppose you select a random sample of 35 Facebook users and record the number of Facebook friends each user has.

A) What is the probability that the 35 Facebook users in your sample have a sample mean number of friends x greater than 177?

(use 4 decimal places in your answer)

B) What is the probability that the 35 Facebook users in your sample have a sample mean number of friends x less than 183?

(use 4 decimal places in your answer)

3. Suppose you’re playing a game where you consecutively roll 3 dice. After each roll you may choose to either roll the next dice or sacrifice one die to reroll any number of the previous dice. If you get a number greater than 5 you win, but if you roll doubles or a number less than 6 you lose.
   1. Considering each roll a separate state what is the approximate branching factor? Justify.
   2. Draw the full state space considering only the number of distinct dice that have been rolled, not what’s on the dice (so if you have rolled one dice and have a 6 that is the same state as if you had rolled a 2). What is the approximate branching factor of this space?
   3. Evaluate the probability of winning for each end state only considering the end state, not the path there.
   4. Using the probability of winning as a heuristic highlight the path of a best first search.

this is all question

A random variable Y whose distribution is binomial with parameters are n = 500 and p= 0.400, and here Y suggests the number of desired outcomes of the random experiment and n-Y is the number of undesired outcomes obtained from a random experiment of n independent trials. On this random experiment   p̂ sample proportion is found as Y/n. (Round your answers to 3 decimal places in all parts.)

a)What is the expected value of this statistic?

b)Between what limits will 99% of the sample proportion occur?

c)What is the probability that sample proportion exceed 0.456?

d). What is the probability that sample proportion less than 0.344?