We are given 3 urns as follows: Urn A contains 3 red and 5 white marbles, Urn B contains 2 red and one white marble, Urn C contains 2 red and 3 white marbles. Construct the probability tree. Suppose that a urn is randomly selected and a marble is drawn from the selected urn. If the marble is red what is the probability that it came from urn A?

Using the weather Markov chain simulate the weather over 10 days by flipping a coin to determine the chances of sunny or cloudy weather the next day according to the Markov chain's transition probabilities. If currently sunny, flip once and a head means sunny the next day and a tail means cloudy the next day. If currently cloudy flip twice and when either flip is a head it is sunny the next day and when both flips are tails it is cloudy the next day. To start, assume that the previous day was sunny. what fraction of the 10 days was sunny?

Test the claim that the proportion of men who own cats is significantly different than the proportion of women who own cats at the 0.2 significance level. The null and alternative hypothesis would be: H 0 : p M = p F H 1 : p M ≠ p F H 0 : μ M = μ F H 1 : μ M < μ F H 0 : μ M = μ F H 1 : μ M > μ F H 0 : μ M = μ F H 1 : μ M ≠ μ F H 0 : p M = p F H 1 : p M < p F H 0 : p M = p F H 1 : p M > p F The test is: left-tailed right-tailed two-tailed Based on a sample of 40 men, 45% owned cats Based on a sample of 40 women, 50% owned cats The test statistic is: (to 2 decimals) The p-value is: (to 2 decimals) Based on this we: Fail to reject the null hypothesis Reject the null hypothesis

In a class of 87 people, 27 wear glasses, 32 are blonde, and 38 are neither blonde nor wear glasses. Find the probability that a student chosen at random will have blonde hair and wear glasses?

The Apex corporation produces corrugated paper. It has collected monthly data from January 2001 through March 2003 on the following two variables:

y= total manufacturing cost per month (In thousands of dollars) (COST)

x= total machine hours used per month (Machine)

The data are shown below.

1102 218
1008 199
1227 249
1395 277
1710 363
1881 399
1924 411
1246 248
1255 259
1314 266
1557 334
1887 401
1204 238
1211 246
1287 259
1451 286
1828 389
1903 404
1997 430
1363 271
1421 286
1543 317
1774 376
1929 415
1317 260
1302 255
1388 281

Answer the following question

Fill in the blanks for the following statement: “I am 95% confident that the average manufacturing cost at the Apex corporation for all months with 350 total machine hours is between ____ and ____.”

please show me steps

You Explain it:

1. What is a residual?
2. What does it mean when a residual is positive?
3. Explain the phrase outside the scope of the model.
4. Why is it dangerous to make predictions outside the scope of the model?
5. Explain what each point on the least-squares regression line represents.

1. 7-31 Consider the following LP problem:

Maximize profit=5X+6Y

subject to2X+Y≤120, 2X+3Y≤240X,Y≥0

1. What is the optimal solution to this problem? Solve it graphically.
2. If a technical breakthrough occurred that raised the profit per unit of X to $8, would this affect the optimal solution?
3. Instead of an increase in the profit coefficient X to $8, suppose that profit was overestimated and should only have been $3. Does this change the optimal solution?

1. 7-32 Consider the LP formulation given in Problem 7-31. If the second constraint is changed from 2X + 3Y≤2402X + 3Y≤240 to 2X+4Y≤240,2X+4Y≤240, what effect will this have on the optimal solution?

"Trydint" bubble-gum company claims that 3 out of 10 people prefer their gum to "Eklypse". Test their claim at the 99 confidence level. The null and alternative hypothesis in symbols would be: H 0 : p ≤ 0.3 H 1 : p > 0.3 H 0 : μ = 0.3 H 1 : μ ≠ 0.3 H 0 : μ ≥ 0.3 H 1 : μ < 0.3 H 0 : μ ≤ 0.3 H 1 : μ > 0.3 H 0 : p = 0.3 H 1 : p ≠ 0.3 H 0 : p ≥ 0.3 H 1 : p < 0.3 The null hypothesis in words would be: The average of people that prefer Trydint gum is not 0.3. The proportion of all people that prefer Trydint gum is less than 0.3. The proportion of people in a sample that prefers Trydint gum is 0.3. The proportion of people in a sample that prefer Trydint gum is not 0.3 The proportion of all people that prefer Trydint gum is greater than 0.3. The proportion of all people that prefer Trydint gum is 0.3 The average of people that prefer Trydint gum is 0.3. Based on a sample of 280 people, 58 said they prefer "Trydint" gum to "Eklypse". The point estimate is: (to 3 decimals) The 99 % confidence interval is: to (to 3 decimals) Based on this we: Reject the null hypothesis Fail to reject the null hypothesis

2. Problem 2 is adapted from the Problem 39 at the end of Chapter 11. Please solve this problem in Excel and submit your Excel spreadsheet. The problem is as follows: The state of Virginia has implemented a Standard of Learning (SOL) test that all public school students must pass before they can graduate from high school. A passing grade is 75. Montgomery County High School administrators want to gauge how well their students might do on the SOL test, but they don't want to take the time to test the whole student population. Instead, they selected 20 students at random and gave them the test. The results are as follows: 83 79 56 93 48 92 37 45 72 71 92 71 66 83 81 80 58 95 67 78 Assume that SOL test scores are normally distributed. a. Compute the mean and standard deviation for these data. b. Determine the probability that a student at the high school will pass the test. c. How many percent of students will receive a score between 75 and 95? d. What score will put a student in the bottom 15% in SOL score among all students who take the test? e. What score will put a student in the top 2% in SOL score among all students who take the test? 3. The average male drinks 2 L of water when active outdoors (with a standard deviation of 0.8L). You are planning a full day nature trip for 100 men and will bring 210 L of water. What is the probability that you will run out? Please solve this problem in Excel and submit your Excel file.

Consider two independent random samples with the following results: n 1 =160 x 1 =84     n 2 =95 x 2 =72 Use this data to find the 90% confidence interval for the true difference between the population proportions. Copy Data Step 1 of 3 : Find the point estimate that should be used in constructing the confidence interval. Round your answer to three decimal places.

in a clinical trial, 25 out of 852 patients taking a prescription drug daily complained of flulike symptoms. Suppose that is it known that 2.5% of patients taking competing drugs complain of flulike symptoms. is there enough evidence to conclude that more than 2.5% of this drugs users experience flulike symptoms as a side effect at the 0.1 level of significance?

Here are summary statistics for randomly selected weights of newborn​ girls: n=187​, x =30.8 ​hg, s=7.9 hg. Construct a confidence interval estimate of the mean. Use a 90​% confidence level. Are these results very different from the confidence interval 29.0 hg-mu-t32.4 hg with only 14 sample​ values, x=30.7 ​hg, and s=3.6 ​hg

At one point the average price of regular unleaded gasoline was $3.53 per gallon. Assume that the standard deviation price per gallon is ​$0.07

per gallon and use​ Chebyshev's inequality to answer the following.

​(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean? What are the gasoline prices that are within 2.5 standard deviations of the​ mean?

​(c) What is the minimum percentage of gasoline stations that had prices between $3.39 and $3.67​?

​(a) At least _​__% of gasoline stations had prices within 3 standard deviations of the mean.(Round to two decimal places as​ needed.)

​(b) At least ___% of gasoline stations had prices within 2.5 standard deviations of the mean.​(Round to two decimal places as​ needed.)

The gasoline prices that are within 2.5 standard deviations of the mean are ​$_to ​$_.​(Use ascending​ order.)

​(c) _​__% is the minimum percentage of gasoline stations that had prices between $ 3.39 and $3.67.

There are 3 coins which when flipped come up heads, respectively, with probabilities 1/4, 1/2, 3/4. One of these coins is randomly chosen and continually flipped.

1. (a) Find the expected number of flips until the first head.

2. (b) Find the mean number of heads in the first 8 flips.