1. In Monopoly, your token is allowed to leave the “jail” cell if you roll doubles: you roll two 6-sided dice and each shows the same face. Zach hates being in jail, because it reminds him of watching “The Wire” on TV. So he invents a couple of weighted dice that are not independent. In particular, if you roll either die on its own it’s a fair die: each outcome has probability 1/6. But if you roll one die and then the other, the red die will take the same outcome as the blue die exactly half the time: all other outcomes are equally likely.

   (a) Suppose you roll a 3 on the blue die. What is the probability distribution of the red die given this outcome on the blue die?

(b) Find the full probability distribution for the value of the sum of the two faces of the dice. (c) What is the probability you roll doubles?

(c) What is the probability you roll doubles?

(d) What is the probability that you roll a 7 as the sum of the two dice?

Given a normal distribution with mu equals 100 and sigma equals 10, complete parts? (a) through? (d). a. What is the probability that Upper X greater than 85 ?? The probability that Upper X greater than 85 is 0.9332 . ?(Round to four decimal places as? needed.) b. What is the probability that Upper X less than 95 ?? The probability that Upper X less than 95 is 0.3085 . ?(Round to four decimal places as? needed.) c. What is the probability that Upper X less than 80 or Upper X greater than 110 ?? The probability that Upper X less than 80 or Upper X greater than 110 is 0.1815 . ?(Round to four decimal places as? needed.)

I need help with d. in bold below

d. 99 ?% of the values are between what two? X-values (symmetrically distributed around the? mean)? 99 ?% of the values are greater than nothing and less than nothing . ?(Round to two decimal places as? needed.)

You are considering the risk-return profile of two mutual funds for investment. The relatively risky fund promises an expected return of 13.7% with a standard deviation of 19.3%. The relatively less risky fund promises an expected return and standard deviation of 3.3% and 6.6%, respectively. Assume that the returns are approximately normally distributed. a-1. Calculate the probability of earning a negative return for each fund. (Round final answer to 4 decimal places.) Probability Riskier fund Less risky fund a-2. Which mutual fund will you pick if your objective is to minimize the probability of earning a negative return? Riskier fund Less risky fund b-1. Calculate the probability of earning a return above 10.2% for each fund. (Round final answer to 4 decimal places.) Probability Riskier fund Less risky fund b-2. Which mutual fund will you pick if your objective is to maximize the probability of earning a return above 10.2%? Riskier fund Less risky fund

You are interested in the probability of the outcome when rolling a six-sided die. Answer the following questions using p to denote the probability of this outcome.

(a) You suspect that for this die the outcome does not occur with the same probability as with a fair die. Formulate the null and alternative hypotheses based on which you may make a statistical inference regarding your suspicion.

(b) You suspect that for this die the outcome occurs with greater probability than with a fair die. Formulate the null and alternative hypotheses based on which you may make a statistical inference regarding your suspicion.

(c) You suspect that for this die the outcome occurs with lesser probability than with a fair die. Formulate the null and alternative hypotheses based on which you may make a statistical inference regarding your suspicion.

(d) You believe that for this die the outcome occurs with the same probability as with a fair die.

How might you collect evidence in support of your belief?

Which is easier: to collect evidence in favor of balancedness or to collect evidence against balancedness?

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 49 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.4 pounds, what is the probability that the sample mean will be each of the following?

Appendix A Statistical Tables

a. More than 60 pounds
b. More than 57 pounds
c. Between 56 and 57 pounds
d. Less than 54 pounds
e. Less than 48 pounds

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

a. enter the probability that the sample mean will be more than 60 pounds

b. enter the probability that the sample mean will be more than 57 pounds

c. enter the probability that the sample mean will be between 56 and 57 pounds

d. enter the probability that the sample mean will be less than 54 pounds

e. enter the probability that the sample mean will be less than 48 pounds

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 50 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following?

Appendix A Statistical Tables

a. More than 61 pounds
b. More than 56 pounds
c. Between 55 and 57 pounds
d. Less than 54 pounds
e. Less than 49 pounds

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

a. enter the probability that the sample mean will be more than 61 pounds

b. enter the probability that the sample mean will be more than 56 pounds

c. enter the probability that the sample mean will be between 55 and 57 pounds

d. enter the probability that the sample mean will be less than 54 pounds

e. enter the probability that the sample mean will be less than 49 pounds

A particular college has a 30% graduation rate. If 212 students are randomly selected, answer the following.

a) Which is the correct wording for the random variable? Select an answer

b) Pick the correct symbol: ? = 212 c) Pick the correct symbol: ? = 0.3

d) What is the probability that exactly 65 of them graduate with a degree? Round final answer to 4 decimal places.

e) What is the probability that less than 65 of them graduate with a degree? Round final answer to 4 decimal places.

f) What is the probability that more than 65 of them graduate with a degree? Round final answer to 4 decimal places.

g) What is the probability that exactly 66 of them graduate with a degree? Round final answer to 4 decimal places.

h) What is the probability that at least 66 of them graduate with a degree? Round final answer to 4 decimal places.

i) What is the probability that at most 66 of them graduate with a degree Round final answer to 4 decimal places

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 50 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following?

Appendix A Statistical Tables

a. More than 58 pounds
b. More than 57 pounds
c. Between 56 and 58 pounds
d. Less than 55 pounds
e. Less than 47 pounds

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

a. enter the probability that the sample mean will be more than 58 pounds

b. enter the probability that the sample mean will be more than 57 pounds

c. enter the probability that the sample mean will be between 56 and 58 pounds

d. enter the probability that the sample mean will be less than 55 pounds

e. enter the probability that the sample mean will be less than 47 pounds

​In a sample of 800 U.S.​ adults, 199 think that most celebrities are good role models. Two Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​ adults, complete parts​ (a) through​ (c).

(a) Find the probability that both adults think most celebrities are good role models. The probability that both adults think most celebrities are good role models is ________?(Round to three decimal places as​ needed.)

​(b) Find the probability that neither adult thinks most celebrities are good role models. The probability that neither adult thinks most celebrities are good role models is _______?(Round to three decimal places as​ needed.) ​

(c) Find the probability that at least one of the two adults thinks most celebrities are good role models. The probability that at least one of the two adults thinks most celebrities are good role models ______? (Round to three decimal places as​ needed.)

You can purchase a certain type of resistor from supplier X, Y or Z. The probability of having a faulty resistor if the resistor was bought from supplier X is 0.02; from supplier Y is 0.05; and from supplier Z is 0.1. Your company purchased a total of 1000 resistors: 300 from supplier X, 500 from supplier Y, and 200 from supplier Z. Use this information to answer the following questions.

1.What is the probability that a randomly selected resistor was purchased from supplier Y?(round to 3 decimals)

2.What is the probability that a randomly selected resistor was purchased from supplier X and is faulty? (round to 3 decimals)

3.What is the probability that a randomly selected resistor is faulty? (round to 3 decimals)

4.What is the probability that a randomly selected resistor is not faulty? (round to 3 decimals)

5.Given that a randomly selected resistor is faulty, what is the probability that it was purchased from supplier Y? (round to 3 decimals)