Question

Given acceleration a(t) = 2i + 3k, with v(0) = 4j.

a) Approximately what proportion of the diameters lie within 2 standard deviations of the mean?

b) Approximately what proportion of the diameters lie within 3 standard deviations of the mean?

Answer 1

Approximately 95% of the diameters lie within 2 standard deviations of the mean, and approximately 99.7% of the diameters lie within 3 standard deviations of the mean.

Step-by-step explanation:

To find the proportion of diameters within 2 standard deviations of the mean, we need to use the concept of the empirical rule. According to the empirical rule, approximately 68% of the data falls within 1 standard deviation of the mean, approximately 95% falls within 2 standard deviations, and approximately 99.7% falls within 3 standard deviations.

So, if we apply this to the given question, approximately 95% of the diameters lie within 2 standard deviations of the mean. For part b, approximately 99.7% of the diameters lie within 3 standard deviations of the mean.