To estimate the percentage of people who took less than 40 seconds to complete the task, let’s break it down:

1. Frequency calculation for each time interval:

   • The area of each bar in the histogram represents the frequency. To calculate the area, use the formula: $\text{Area} = \text{Frequency Density} \times \text{Width of the interval}.$

2. Identify intervals and calculate areas:

   • For 0–10 seconds: Frequency Density = 40, Width = 10 $\text{Area} = 40 \times 10 = 400.$
   • For 10–20 seconds: Frequency Density = 35, Width = 10 $\text{Area} = 35 \times 10 = 350.$
   • For 20–30 seconds: Frequency Density = 25, Width = 10 $\text{Area} = 25 \times 10 = 250.$
   • For 30–40 seconds: Frequency Density = 15, Width = 10 $\text{Area} = 15 \times 10 = 150.$

   Total frequency for 0–40 seconds: $400 + 350 + 250 + 150 = 1150.$

3. Calculate the total frequency for all intervals:

   • For 40–50 seconds: Frequency Density = 10, Width = 10 $\text{Area} = 10 \times 10 = 100.$

   Total frequency: $1150 + 100 = 1250.$

4. Percentage of people who took less than 40 seconds: $\text{Percentage} = \frac{\text{Frequency for 0–40 seconds}}{\text{Total Frequency}} \times 100 = \frac{1150}{1250} \times 100 = 92.0\%.$

Final Answer:

The percentage of people who took less than 40 seconds to complete the task is 92.0%.

Let me know if you have any questions or need further clarifications!

Related Questions:

1. How do you calculate frequency density in histograms?
2. What does the area of a histogram bar represent in terms of data?
3. Can histograms be used for non-continuous data? Why or why not?
4. How would the result change if the total interval widths were unequal?
5. What are some practical uses of histograms in data analysis?

Tip:

When analyzing histograms, always ensure you check if the interval widths are equal to simplify calculations or adjust the calculations accordingly if they vary.