Answer:
To find the probability that the lunch costs between $7 and $8, we need to use the information provided by the uniform density curve.
1. The uniform density curve represents a constant probability distribution, where all values within a certain range have an equal chance of occurring.
2. Since the density curve is uniform, the probability of selecting a lunch that costs between $7 and $8 is the same as the proportion of the total area under the curve within that range.
3. To calculate this probability, we need to determine the area under the curve between $7 and $8.
4. Since the density curve is uniform, the height of the curve is constant throughout the range.
5. The width of the range is $8 - $7 = $1.
6. The area of a rectangle is calculated by multiplying the base (width) by the height.
7. Therefore, the area under the curve between $7 and $8 is $1 multiplied by the height of the curve.
8. Since the curve is uniform, the height is constant, so the area is simply $1 multiplied by the height.
9. The probability of selecting a lunch that costs between $7 and $8 is equal to the area under the curve between $7 and $8, divided by the total area under the curve.
10. Since the total area under the curve represents all possible lunch costs, the total area is equal to 1.
11. Therefore, the probability of selecting a lunch that costs between $7 and $8 is equal to the area under the curve between $7 and $8, divided by 1.
12. In conclusion, the probability that the lunch costs between $7 and $8 is equal to the height of the curve, which is a constant value for the uniform density curve.
