A student recently took a statistics exam and the professor has posted that the mean was 67 % with a standard deviation of 9 %. The professor will hand out the exams at the beginning of next week, however, this student decides to calculate a few quantities to hopefully ease their mind. a) What is the probability that they scored above 70%? (round to four decimal places) b) What is the probability that they scored below 60%? (round to four decimal places) c) What is the probability that they scored between 70-90%? (round to four decimal places)
A student recently took a statistics exam and the professor has posted that the mean was 67 % with a standard deviation of 9 %. The professor will hand out the exams at the beginning of next week, however, this student decides to calculate a few quantities to hopefully ease their mind.
a) What is the
b) What is the probability that they scored below 60%? (round to four decimal places)
c) What is the probability that they scored between 70-90%? (round to four decimal places)
d) Would the probability of the student passing the test (score above 70%) increase or decrease if the mean increased and the standard deviation stayed the same? Justify your answer.
e) Would the probability of the student passing the test (score above 70%) increase or decrease if the mean stayed the same and the standard deviation increased? Justify your answer.
f) Suppose that both the mean increased and standard deviation increased. Does the student's probability of passing the exam:
- definitely increase
- definitely decrease
- can either decrease or increase
Justify your answer.
g) Suppose that both the mean increased and standard deviation decreased. Does the student's probability of passing the exam:
- definitely increase
- definitely decrease
- can either decrease or increase
Justify your answer.
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