A set of final examination grades in an introductory statistics course is normal

Question

A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 74 and a standard deviation of 8. Complete parts (a) through (d). a. What is the probability that a student scored below 83 on this exam? The probability that a student scored below 83 is. b. What is the probability that a student scored between 66 and 93? The probability that a student scored between 66 and 93 is. c. The probability is 25% that a student taking the test scores higher than what grade? The probability is 25% that a student taking the test scores higher than. d. If the professor grades on a curve (for example, the professor could give A's to the top 10% of the class, regardless of the score), is a student better off with a grade of 82 on this exam or a grade of 77 on a different exam, where the mean is 69 and the standard deviation is 4? Show your answer statistically and explain. A student is with a grade of 82 on this exam because the Z value for the grade of 82 is and the Z value for the grade of 77 is .

Explanation / Answer

a)P(X<83)=P(Z<(83-74)/8)=P(Z<1.125)=0.8697

b)P(66<X<93)=P(-1<Z<2.375)=0.9912-0.1587=0.8326

c)for 75 percentile z=0.6745

hence corresponding socere=79.40~79

d)z value for the grade of 82=3.25 and that for 77 is 2.

please reply with options for part d

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