Question

A set of final examination grades in an introductory statistics course is normally​ distributed, with a...

A set of final examination grades in an introductory statistics course is normally​ distributed, with a mean of 73 and a standard deviation of 7. Complete parts​ (a) through​ (d).

a. What is the probability that a student scored below 86 on this​ exam?

​(Round to four decimal places as​ needed.)

b. What is the probability that a student scored between 66 and 93​?

​(Round to four decimal places as​ needed.)

c. The probability is 55​% that a student taking the test scores higher than what​ grade?

​(Round to the nearest integer as​ needed.)

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

80 on this exam or a grade of 74 on a different​ exam, where the mean is 68 and the standard deviation is 3​?

Show your answer statistically and explain.

A student is

worse off

better off

with a grade of 80 on this exam because the Z value for the grade of 80 is ________  and the Z value for the grade of 74 is ___________

​(Round to two decimal places as​ needed.)

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