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Question 5 of 5

A community activist is gathering data to support an initiative to have a traffic light constructed at a busy intersection near a school. On average, 100 vehicles pass through the intersection daily during the time when students are traveling to school. The initiative for the traffic light is based on promoting safety, as supporters feel vehicles pass through the intersection at dangerously high speeds.

The activist wants to know the average speed at which vehicles pass through the intersection during this critical time. He randomly picked 20 vehicles during the time when students are traveling to school, assuming that these 20 vehicles accurately represented all vehicles that pass through the intersection during the critical time. He recorded their speed as they passed through the intersection with a radar speed gun. The speeds collected, given in miles per hour, are shown in the table below.

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|}
\hline \multicolumn{8}{|c|}{Speeds (miles per hour)} \\
\hline 32 & 20 & 41 & 38 & 35 & 28 & 25 & 18 & 30 & 27 \\
\hline 31 & 15 & 35 & 37 & 32 & 28 & 25 & 33 & 32 & 30 \\
\hline
\end{tabular}

Can the approximate speed for all of the cars that pass through the intersection during this critical time be calculated from the given data? If so, calculate it. Non-integer answers should be rounded to the nearest tenth. If no assumption can be made, type [tex]$0^{-5}$[/tex] in the box.

The approximate speed for all of the cars that pass through the intersection during this critical time is [tex]\square[/tex] miles per hour.

Sagot :

GinnyAnsweridn
To determine the approximate speed for all the cars that pass through the intersection during the critical time, we need to calculate the average speed of the given sample of 20 vehicles.

Here are the recorded speeds in miles per hour:
32, 20, 41, 38, 35, 28, 25, 18, 30, 27, 31, 15, 35, 37, 32, 28, 25, 33, 32, 30.

To calculate the average speed, follow these steps:

1. Sum the recorded speeds:
- Add together all the speeds:
[tex]\( 32 + 20 + 41 + 38 + 35 + 28 + 25 + 18 + 30 + 27 + 31 + 15 + 35 + 37 + 32 + 28 + 25 + 33 + 32 + 30 \)[/tex]

2. Count the number of speeds:
- The number of recorded speeds is 20.

3. Calculate the average speed:
- Divide the total sum by the number of speeds:
[tex]\( \text{Average speed} = \frac{\text{Sum of all speeds}}{\text{Number of speeds}} \)[/tex]

4. Round the result to the nearest tenth:
- If the result is not an integer, round it to one decimal place.

Given the detailed solution, we find:

- The total sum of the speeds is 592.
- The number of speeds is 20.
- The average speed is:
[tex]\( \frac{592}{20} = 29.6 \)[/tex]

Therefore, the approximate speed for all the cars that pass through the intersection during this critical time is [tex]\( \boxed{29.6} \)[/tex] miles per hour.
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