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Answer:
(a) The percentage of the scores were less than 59% is 16%.
(b) The percentage of the scores were over 83% is 2%.
(c) The number of students who received a score over 75% is 26.
Step-by-step explanation:
Let the random variable <em>X</em> represent the scores on a Psychology exam.
The random variable <em>X</em> follows a Normal distribution with mean, <em>μ</em> = 67 and standard deviation, <em>σ</em> = 8.
Assume that the maximum score is 100.
(a)
Compute the probability of the scores that were less than 59% as follows:
*Use a <em>z</em>-table.
Thus, the percentage of the scores were less than 59% is 16%.
(b)
Compute the probability of the scores that were over 83% as follows:
*Use a <em>z</em>-table.
Thus, the percentage of the scores were over 83% is 2%.
(c)
It is provided <em>n</em> = 160 students took the exam.
Compute the probability of the scores that were over 75% as follows:
The percentage of students who received a score over 75% is 16%.
Compute the number of students who received a score over 75% as follows:
Thus, the number of students who received a score over 75% is 26.