A sample of 500 evening students revealed that their annual incomes from employment in industry during the day were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. (i) 250 students earned more than $30,000.
(ii. 341 students earned between $27,000 and $33,000.
(iii) 239 students earned between $24,000 and $30,000.
A) (i), (ii), and (iii) are all correct statements.
B) (i) is a correct statement but not (ii) or (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (i) and (ii) are correct statements but not (iii).
E) (ii) and (iii) are correct statements but not (i).

Question

Quizplus · Accepted Answer

(i) 250 students earned more than $30,000, which means they are above the mean of $30,000, so it is correct.
(ii) The interval of $27,000 to $33,000 contains the mean of $30,000 and is within one standard deviation of the mean. Since the normal distribution is symmetric, we can assume that approximately 68% of the students' incomes fall within one standard deviation of the mean. Therefore, it is correct.
(iii) The interval of $24,000 to $30,000 also contains the mean of $30,000 and is within one standard deviation of the mean. As explained in (ii), approximately 68% of the students' incomes fall within one standard deviation of the mean, so it is correct.

A Sample of 500 Evening Students Revealed That Their Annual