Assignment 4ATotal Marks = 75Please show all your work. Some questions require you to use graphs, treediagrams, formulas, and so on that are difficult or impossible to reproducein word-processing programs, so you will have to print the entireassignment and fill it out and mail it to your tutor. As an alternative tomailing, you might be able to photograph or scan your assignment andsubmit it through the appropriate drop box. If you do, make sure thematerial you are submitting is legible.Question 1Grade point averages of math majors at a large distance educationuniversity are normally distributed with a mean of = 2.85 and a standarddeviation of = 0.30 . If a random sample of 25 math majors is selectedfrom that university, what is the probability that the sample mean gradepoint average will be6 marksa.either less than 2.709 or more than 2.955?3 marksb. at least 2.757?a) P(x < 2.709) or P(x>2.955) = P(x <2.709> <2.955> <2.709 :="P(x">2.955): ===2.7092.850.3/252.9552.850.3/25= 2.35. ( < 2.35) = 0.0094= 1.75 P(z>1.75) = 0.9599Total Probability = 0.0095+1-0.9599 = 0.0496b) P(x>2.757) = 1-P(x <2.757>< 1.55) = 0.0606 =0.325Probability = 1-0.0606 = 0.9394Introduction to Statistics1Question 2Psychologists estimate that 80% of male drivers, when lost in t ...
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