Question

most roller coasters get their speed by dropping down a steep initial incline, so it makes sense that the height of that drop might be related to the speed of the coaster. heres a scatterplot of top speed and largest drop for 75 coasters around the world. complete parts a) and b). b) in fact, the correlation of speed and drop is 0.90. describe the association. choose the correct answer below. a. there is a strong, negative, linear association between drop and speed; the smaller the coasters initial drop, the higher the top speed. b. there is a strong, positive, linear association between drop and speed; the greater the coasters initial drop, the higher the top speed. c. there is a weak, negative, linear association between drop and speed; the smaller the coasters initial drop, the higher the top speed.

Explanation:

Step1: Understand correlation coefficient

A correlation coefficient of 0.90 indicates a strong positive linear relationship. When the correlation coefficient \(r\) is close to 1, as \(r = 0.90\) here, as one variable (drop height) increases, the other variable (top - speed) also increases.

Step2: Analyze the relationship

In the context of roller - coasters, a strong positive linear association means that the greater the initial drop (height of the drop), the higher the top speed of the coaster.

Answer:

B. There is a strong, positive, linear association between drop and speed; the greater the coaster's initial drop, the higher the top speed.