Question

1. the mean speed of vehicles in the \cars only\ lanes of the new jersey turnpike is 68 mph. the mean speed of vehicles in the \any vehicle\ lanes is 64 mph. what must be true about the mean speed of all vehicles on the turnpike, assuming these are the only types of lanes? a. it could be any number from 64 to 68 mph. b. it must be larger than the median speed. c. it must be larger than 66 mph. d. it must be 66 mph.

Explanation:

Step1: Recall the formula for combined mean

Let \(n_1\) be the number of vehicles in "cars only" lanes and \(n_2\) be the number of vehicles in "any vehicle" lanes. The combined mean \(\bar{x}=\frac{n_1\times68 + n_2\times64}{n_1 + n_2}\).

Step2: Simplify the combined - mean formula

$$
LATEXBLOCK0
$$

Since \(n_1>0\) and \(n_2\geq0\), when \(n_2 = 0\), \(\bar{x}=68\) (upper - bound). When \(n_1 = 0\), \(\bar{x}=64\) (lower - bound). But \(n_1>0\) (because there are vehicles in "cars only" lanes), so \(64<\bar{x}\leq68\).

Answer:

A. It could be any number from 64 to 68 mph.