work on the question below

You are at a table at a casino with a gambling game. In the game you spin two spinners. Spinner #1 has 4 equal spaces numbered 1,2,3,4. Spinner #2, has only two equal spaces with the numbers 1 and 3.To play the game, you have to pay $4 dollars. Regardless of whether you win or lose you have to pay the $4. There are two different bets you can make that are related to the sum of the two spins (number from Spinner #1 + number from Spinner #2).Shown below are the two different bets and amounts associated with winning each.

Bet 1: You win $8 if the sum of Spinner #1 and Spinner #2 is less than 5

Bet 2: You win $12 if the sum of Spinner #1 and Spinner #2 is greater than 5

What is the sample space? Hint: this is the number of different outcomes where order does matter. So getting a 1 on Spinner #1 and 3 on Spinner #2 is a distinct outcome from the reverse.

What is the probability of winning Bet 1? What is the probability of winning Bet 2?

What is the expected value of Bet 1? What is the expected value of Bet 2? Which is the better bet? Would you break even (i.e. not lose any money) with either bet?

For Bet 2, how much would you have to earn to exactly break even (neither lose nor win money in expectation)?

Now imagine for Bet 1 you only have to pay the $4 to play if you lose. What is the expected value of Bet 1 now? Would you break even?

2. An analyst wished to gauge the contrast between the extent of clients of two

shampoos who are happy with the prodcut. In an example of 400 clients of Shampoo A

taken by this specialist, 78 said they are satisifed. In another example of 500 clients of

Cleanser B taken by a similar analyst, 92 said they were fulfilled.

a) Construct a 90% certainty stretch for the genuine distinction between the two populace

extents.

b) Based on your answer in (a), what might be your reaction at "=0.1 to the case that

there is no distinction in consumer loyalty between the two shampoos?

3. An overview as of late announced that the mean public yearly consumption for inpatient and

outpatient administrations of all people more than 64 years old was $5,423 with a norm

deviation of $979. An irregular example of 352 people over age 64 living in Sudbury had an

normal cost of $5,516.

a) Can we presume that the mean inpatient and outpatient cost of all Sudbury

inhabitants over age 64 is higher than the public normal of $5,423? Utilize the .01

level of importance.

b) Calculate the P-an incentive for this test. Would your answer have changed on the off chance that you had utilized a

.05 degree of importance?

A report states that the mean yearly salary offer for students graduating with mathematics and statistics degrees Is $52,965. Suppose that a random sample of 50 mathematics and statistics graduates at a large university who received job offers resulted In a mean offer of $63,600 and a standard deviation of $3,600. Do the sample data provide strong support for the claim that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,9657 Test the relevant hypotheses using a = 0.05. In USE SALT Find the test statistic and P-value. (Use technology to calculate the Pivalue. Round your test statistic to two decimal places and your P-value to three decimal places.) P-value m State your conclusion. Fail to reject Me. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,965. Reject Me. We do not have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,965. @Fail to reject N. We do not have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,965. Reject No. We have convincing evidence that the mean salary offer for mathematics and statistics graduates of this university is greater than the national average of $62,965.Finite Mathematics Quiz (Probability I, Chapter 7) Show your calculations to receive any credit! The table shows funding sources for research and development (dollars in billions). Find the probability that the funds for a particular project came from Academic Institutions or Industry. Source Amount ('S in billions) Federal Government 103.7 State and Local Government 3.5 Industry 267.8 = P(Academic institutions or Industry) Academic Institutions 10.6 Other 12.0 TOTAL 397.6A study of high school juniors in three districts - Belvidere, Rockford, and Byron - was conducted to determine enrollment trends in AP mathematics courses - Calculus or Statistics. 42% of students in the study came from Rockford, 37% from Belvidere, and the rest from Bryon. In Rockford, 64%% of the juniors took Statistics and the rest took Calculus. 58% of juniors in Belvidere and 49% of juniors in Byron took Statistics while the rest took Calculus in each district. No juniors took both Statistics and Calculus. a. Describe this situation using a tree diagram. (3 marks) b.Find the probability that a randomly selected student from in the study took Statistics. (2 marks)c. If I weighed 15 pounds more than I do, what percentile would I be in? A production process manufactures items with weights that are normally distributed with mean 10 pounds and standard deviation 0.1. An item is considered to be defective if its weight is less than 9.8 pounds or greater than 10.2 pounds. Suppose that these items are currently produced in batches of 1000 units. a. Find the probability that at most 5% of the items in a given batch will be defective b. Find the probability that at least 85% of these items in a given batch will be acceptable. O Mathematical Statistics Probability and Solutions Probability and textbook with Applications Statistics for Engineers Statistics for 7th Edition 9th Edition Oth Edition