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# In a population of people, the true mean salary

In a population of people, the true mean salary is 60,000 per year. assuming salaries are normally distributed what is the probability that an alumnus drawn at random will have a salary greater than \$100,000? assume standard deviation of 40,000.You survey a random sample of 100 people about their salaries. You estimate a mean salary Y of 75,000 per year and standard deviation of s= 30,000.a. what is the bias of the Y bar estimator? please show this (prove it!)b. you want to test (using your sample) if the mean salary of UCD alumni is \$100,000. What is your null hypothesis? what is your alternative hypothesis?c. to test your hypothesis, you decided to test the .05 level of significance. please set up your test statistic.d. what distribution did you use? why did you use it?3. Please rewrite each of the following as a function of means (?x, ?y,?z), variances (?x,?y,?z) and/or covariances (?xy, ?yz, ?xz). E(.), V(.), COV(.) are the expectation, variance and covariance operators, respectively, and a,b,c and d are constants.a. E(a+bX+cY)b. V(a+bX+dZ)c. V(bX+dZ)Must show work on all