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Type the correct answer in the box. Use numerals instead of words.

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 represent all vehicles that pass through the intersection during this 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 "0" 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.



Answer :

GinnyAnswer
Certainly! Let's determine the approximate speed for all of the cars that pass through the intersection during the critical time using the speeds recorded.

Here are the steps involved:

1. List the recorded speeds:
[tex]\[ 32, 20, 41, 38, 35, 28, 25, 18, 30, 27, 31, 15, 35, 37, 32, 28, 25, 33, 32, 30 \][/tex]

2. Calculate the sum of the speeds:
The total sum of these speeds is [tex]\(592\)[/tex] miles per hour.

3. Count the number of speeds recorded:
There are [tex]\(20\)[/tex] speeds recorded.

4. Calculate the mean (average) speed:
To find the mean speed, we divide the total sum of the speeds by the number of speeds recorded:
[tex]\[ \text{Mean Speed} = \frac{\text{Total Sum of Speeds}}{\text{Number of Speeds}} = \frac{592}{20} = 29.6 \, \text{miles per hour} \][/tex]

5. Round the mean speed to the nearest tenth:
The mean speed after rounding to the nearest tenth is [tex]\(29.6\)[/tex] miles per hour.

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

So, the correct answer to be typed in the box is:
[tex]\[ 29.6 \][/tex]

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