Final answer:
The upper-class boundary for the 5-6 minute interval is 5.5 minutes. The height of the second tallest bar in the histogram is 10 cm. The estimated number of people with a waiting time between 3.5 minutes and 7 minutes is 31. The median of the waiting times is estimated to be 12.67 minutes.
Step-by-step explanation:
To find the upper-class boundary for the 5-6 minute interval, we need to subtract 0.5 from the upper limit of the interval. In this case, the upper limit is 6, so the upper-class boundary is 6 - 0.5 = 5.5 minutes.
To calculate the height of the second tallest bar in the histogram, we need to find the frequency of the corresponding interval. In this case, the interval is 9-10, and the frequency is 10. So, the height of the second tallest bar is 10 cm.
To estimate the number of people with a waiting time between 3.5 minutes and 7 minutes, we need to sum up the frequencies of the intervals that fall within this range. In this case, the intervals are 3.5-4, 4-5, and 5-6, with frequencies 0, 21, and 10 respectively. So, the estimated number of people is 0 + 21 + 10 = 31.
To estimate the median of the waiting times using linear interpolation, we first need to calculate the total number of observations, which is the sum of all the frequencies, i.e., 21 + 10 + 10 + 30 + 18 = 89. The cumulative frequency just before the median is reached is (89 + 1) / 2 = 45. The interval containing the median is 11-15, so the lower limit of this interval is 11. The width of the interval is 15 - 11 = 4. Using the formula for linear interpolation, we have:
Median = lower limit + [(45 - cumulative frequency of previous interval) / frequency of median interval] * interval width = 11 + [(45 - 10) / 30] * 4 = 12.67 minutes.