Question

Exam scores in a large calculus course follow a uniform distribution on the interval from 18 to 98. what proportion of students have scores within 15 marks of the mean?

(a) 0.325
(b) 0.350
(c) 0.375
(d) 0.400
(e) 0.425

Answer 1

The proportion of students with scores within 15 marks of the mean is 0.375. Option c

Step-by-step explanation:

To find the proportion of students with scores within 15 marks of the mean, we need to calculate the range of scores that fall within this interval.

The mean of the uniform distribution is given by the formula (lower bound + upper bound) / 2. In this case, the mean is (18 + 98) / 2 = 58.

The range of scores within 15 marks of the mean is from 58 - 15 = 43 to 58 + 15 = 73. To calculate the proportion of students within this range, we divide the length of the range (73 - 43 = 30) by the total length of the distribution (98 - 18 = 80).

The proportion of students with scores within 15 marks of the mean is 30 / 80 = 0.375. Option c