ercise 34.10. The students in my class have Exam 1 scores which are Normally str

Question

ercise 34.10. The students in my class have Exam 1 scores which are Normally stributed with a mean of 75 and a standard deviation of 9. If a student is selected attrandom a What is the probability the student will have a score of more than 90 (an A)? b What is the probability the student will have a score of less than 60 (an F)? What is the probability a student will have a score between 80 and 89 (the B e)? what is the range of scores for the middle 50% of the student scores? e. What is the range for the central 99.7% of the scores? f What is the lower cut-off for the top 3/4 of the students?

Explanation / Answer

Since =75 and =9 we have:

P ( X>90 )=P ( X>9075 )=P ( X>90759)

(a)

Since Z = x / and (9075) / 9 = 1.67 we have:

P ( X > 90 ) = P ( Z > 1.67 )

Use the standard normal table to conclude that:

P (Z > 1.67) = 0.0475

(b)

Since = 75 and = 9 we have:

P ( X < 60 ) = P ( X < 6075 ) = P (X / < (6075) / 9)

P (X < 60) = P (Z < 1.67)

Using the standard normal table to conclude that:

P (Z < 1.67) = 0.0475

(c)

Since Z = x / , (8075) / 9 = 0.56 and (8975) / 9 = 1.56 we have:

P ( 80 < X < 89 ) = P ( 0.56 < Z < 1.56 )

Using the standard normal table to conclude that:

P ( 0.56 < Z < 1.56 ) = 0.2283

(d)

For 50% it is 75 marks.

(e)

For 99.7% it is 99.730 marks.

(f) Top 3/4 is 75% is 81.070.

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