Answer all questions and please show step by step for explanation, please and thank you.

1) A wood manufacturer must decide whether to merge with a larger company to make more investments. If they merge and it is a good sales year, there will be a $910,000 profit; if they merge and it is a poor sales year, there will be a deficit of $ 330,000. If they do not merge and it is a good sales year there will be a $525,000 profit; if they do not merge and it is a poor sales year there will be a $97,000 profit. If the probability of a good sales year is 0.26 and the probability of a poor sales year is 0.76, would merging with the larger company maximize the expected profit?

2) A survey at a restaurant in small western town yielded the data below:

Married Single Divorced

Travelers 24 20 3

Non-Travelers 14 7 1

a)If we randomly select one person, what is the probability that a non-traveler and a single is selected? Write your answer as a percentage.

b)If we randomly select one person, what is the probability of selecting a traveler or not a married? Write your answer as a percentage.

c) If we randomly select one person, what is the probability of selecting a traveler, given that it was divorced? Write your answer as a percentage.

3.What does Chebyshev'stheorem with k=12 tells us about the number of heads that we may get in 900 flips of a balanced coin?

4.In a mountain area where mines have to be tested for the emission of pollutants, 32% of all mines emit excessive amounts of pollutants. When tested, 98% of all mines that emit excessive amount of pollutants will fail, but 21% of the mines that do not emit excessive amounts of pollutants will also fail. What is the probability that a mine that fails the test actually emits excessive amounts of pollutants?

5.A sample of 800 truck drivers from Minnesota were interviewed randomly and 316 answered they like tunnels. Determine if the sample evidence shows that less than half of the truck drivers like tunnels. Use =0.05.

6. A simple random sample of 19models' runnawayis obtained, providing a standard deviation of 11.19. Construct a 90% confidence interval for , thestandard deviation from which the sample was obtained.

7. The result of a sample study in a private school provided that 68 STEM major students average 13.8 math study hours with a standard deviation of 4.7 in a given month, while 54 students average 10.2 with a standard deviation of 6.5. Test at the 0.01 level of significance if the means of the two sample means are the same.

8. Monthly salary computations from two different clothing companies yielded the following data:= , =9,130$,=386$;= , =8,840$,=212$. At the level of significance 0.05, can we conclude that the mean monthly salary from the two companie is not the same?