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Answer :
The estimated percentage of 35 people who took less than 40 seconds to complete the task is approximately 29.2%.
To estimate the percentage of people who took less than 40 seconds to complete the task, we need to analyze the histogram provided. The histogram displays the frequency density of the time taken to complete the task in seconds.
Looking at the histogram, we can see that the bin representing the time range of 35-40 seconds has a frequency density of 15. This means that 15 people fall within this time range.
To estimate the percentage, we need to calculate the cumulative frequency. The cumulative frequency represents the number of people who took less than or equal to a certain time. In this case, we are interested in the cumulative frequency of the bin representing the time range of 0-40 seconds.
To calculate the cumulative frequency, we sum up the frequency densities of all the bins up to and including the bin of interest. In this case, we add up the frequency densities of the bins representing the time ranges of 0-5, 5-10, 10-15, 15-20, 20-25, 25-30, 30-35, and 35-40 seconds.
Adding up the frequency densities, we get:
0 + 5 + 10 + 15 + 20 + 25 + 30 + 15 = 120
The cumulative frequency for the time range of 0-40 seconds is 120. Since we are interested in the percentage of 35 people, we divide the cumulative frequency of 35 by the total cumulative frequency and multiply by 100.
Percentage = (35 / 120) * 100 ≈ 29.2%
Therefore, the estimated percentage of 35 people who took less than 40 seconds to complete the task is approximately 29.2%.
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