Every day a school bus driver passes the same traffic light twice, once before school and once after.Each time he passes the light, he records if it is red, green, or yellow.Here is a summary of the data he got after 200 days.Traffic light before school Traffic light after school Number of daysred red 33red green 23red yellow 28green red 17green green 34green yellow 13yellow red 21yellow green 15yellow yellow 16Suppose the driver will continue recording the colors for 150 more days.In how many of these 150 days will the light be green exactly once? Use the data to make a prediction.
Question
Every day a school bus driver passes the same traffic light twice, once before school and once after.Each time he passes the light, he records if it is red, green, or yellow.Here is a summary of the data he got after 200 days.Traffic light before school Traffic light after school Number of daysred red 33red green 23red yellow 28green red 17green green 34green yellow 13yellow red 21yellow green 15yellow yellow 16Suppose the driver will continue recording the colors for 150 more days.In how many of these 150 days will the light be green exactly once? Use the data to make a prediction.
Solution
To predict the number of days the light will be green exactly once in the next 150 days, we need to find the proportion of days this occurred in the original 200 days and apply that proportion to the next 150 days.
From the data, we can see that the light was green exactly once on the following days:
- Red before school and green after school: 23 days
- Green before school and red after school: 17 days
- Yellow before school and green after school: 15 days
- Green before school and yellow after school: 13 days
So, the total number of days the light was green exactly once in 200 days is 23 + 17 + 15 + 13 = 68 days.
The proportion of days the light was green exactly once is 68/200 = 0.34 (or 34%).
If we apply this proportion to the next 150 days, we can predict that the light will be green exactly once on 0.34 * 150 = 51 days.
So, we predict that the light will be green exactly once on 51 of the next 150 days.
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