For a Special Report in the Cedar Rapids, IA, Gazette

question 21

Essay

For a special report in the Cedar Rapids, IA, Gazette, reporters used a radar gun to
check the speeds of 1,239 drivers in two counties. They were shocked (!) to discover
that some drivers were driving at a speed greater than the posted limits. They
reported the following information in their story: $$\begin{array}{l}\text { Speeding data for cities in Linn and Johnson Counties }\\\begin{array} { | l | c | c | c | c | } \hline \text { City } & \begin{array} { l } \text { City } \\\text { Speed } \\\text { Limit }\end{array} & \begin{array} { l } \text { Drivers } \\\text { Observed }\end{array} & \begin{array} { l } \text { Over } \\\text { Limit }\end{array} & \begin{array} { l } \text { \%Over } \\\text { Limit }\end{array} \\\hline \text { Cedar Rapids } & 25 & 241 & 233 & 96.7 \\\text { Iowa City } & 35 & 292 & 124 & 42.5 \\\text { Iowa City } & 20 & 203 & 203 & 100.0 \\\text { Marion } & 30 & 329 & 268 & 81.5 \\\text { Coralville } & 25 & 174 & 161 & 92.5 \\\hline\end{array}\end{array}$$ Suppose that one of these drivers is selected at random. Define the following events:
F = the event that a randomly selected driver was in the fast lane (speed limit
above 25 mph)
S = the event that a randomly selected driver is speeding.
a) The table below shows the possible combinations of F and S. For each
combination, calculate the probability that the combination would be observed for
a randomly selected driver. Enter these probabilities into the corresponding cell in
the table. $$\begin{array} { | l | c | c | } \hline & \begin{array} { c } \text { Speed Limit } \\> 25 \mathrm { mph } \\\text { (Fast lane) }\end{array} & \begin{array} { c } \text { Speed Limit } \\\text { 25mph or less } \\\text { (Slow lane) }\end{array} \\\hline \text { Driver speeding } & & \\\hline \text { Driver not speeding } & & \\\hline\end{array}$$ $$\text { b) Using the information in your table from part (a), calculate } P ( F \cup S ) \text {. }$$ $$\text { c) Using the information in your table from part (a), calculate } P \left( S ^ { C } \right)$$

---

Definitions:

Toyota

A multinational automotive manufacturer headquartered in Japan, known for its cars and innovation in the industry.

Null Hypothesis

A statement or hypothesis that there is no significant difference or effect, used as a default assumption in statistical hypothesis testing.

One-way ANOVA

A statistical test that compares the means of three or more independent groups to determine if there is a significant difference between them, based on a single independent variable.

Drug Experimentation

The process of testing and evaluating the effects, safety, and efficacy of pharmaceutical substances in controlled environments.