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.

1. which of the following distributions has the smallest standard deviation?

(a)
(b)
(c)
(d)

Explanation:

Step1: Recall the concept of standard deviation

Standard deviation measures the spread of data. A smaller standard deviation means the data is more clustered around the mean.

Step2: Analyze each distribution

• Distribution (a): Data is spread out with no clear clustering.
• Distribution (b): Uniform distribution (all frequencies are the same), so data is spread evenly.
• Distribution (c): Bell - shaped but not as tightly clustered as (d).
• Distribution (d): Tightly clustered around the center (around \(x = 6\)).

Answer:

d.