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Going back to problem 1, in real life you can, without muchdifficulty, get the mean grade of Prof. Lax’s classes but that isabout it; meaning you will have no idea how his grades would bedistributed, nor would you have any idea about the standarddeviation of these grades. (I doubt Prof. Lax would advertise hislaxness on his website. Contrary what you might believe that isacademically bad form and might negatively affect his students’hireability in the job market). However, you have access to MissZ’s data (which she swears is obtained by a random selectionprocess) and the grades she obtained in her random sample of ninewere: 79, 75, 84, 63, 98, 52, 87, 99, 83 a. To help Miss Z with herdecision to take this course with Prof. Lax or not, create a 97%confidence interval (CI) for the mean using Miss Z.’s data. Makesure that you do the necessary checks. b. Does your intervalcapture the rumored population mean of 85? c. Calculate the marginof error (ME or simply E) of your confidence interval. d. Miss Zthinks a margin of error (or E) of 7 points or more will have asignificant negative effect on her GPA. How does the ME (or E) ofyour 97% CI from part (c) compare to what she says her GPA canafford? If your CI’s ME (or E) is different than 7 points she canafford what are the ways you can use to reduce the margin of errordown to 7 or smaller. Discuss all that can be done.