Question

a. Determine the percentage of finishers with times between 50 and 75 minutes. Approximately ___ % of finishers had times between 50 and 75 minutes. (Round to two decimal places as needed.) b. Determine the percentage of finishers with times less than 80 minutes. pproximately ___ % of finishers had times less than 80 minutes. (Round to two decimal places as needed.) c. Obtain and interpret the 40th percentile for the finishing times. The 40th percentile is___ minutes. (Round to two decimal places as needed.) Interpret the 40th percentile. Select the correct choice below and fill in the answer box(es) to complete your choice. (Type integers or decimals rounded to two decimal places as needed.)

Answer 1

a. To determine the percentage of finishers with times between 50 and 75 minutes, we need to find the proportion of finishers with times in that range and convert it to a percentage. From the cumulative frequency table, we see that the number of finishers with times between 50 and 75 minutes is 75 - 45 = 30. The total number of finishers is 100. Therefore, the proportion of finishers with times between 50 and 75 minutes is 30/100 = 0.3. To convert this to a percentage, we multiply by 100 and get 30%.

Approximately 30% of finishers had times between 50 and 75 minutes.

b. To determine the percentage of finishers with times less than 80 minutes, we need to find the proportion of finishers with times less than 80 minutes and convert it to a percentage. From the cumulative frequency table, we see that the number of finishers with times less than 80 minutes is 95. The total number of finishers is 100. Therefore, the proportion of finishers with times less than 80 minutes is 95/100 = 0.95. To convert this to a percentage, we multiply by 100 and get 95%.

Approximately 95% of finishers had times less than 80 minutes.

c. The 40th percentile is the value that separates the lowest 40% of the finishers from the highest 60%. From the cumulative frequency table, we see that the value corresponding to the 40th percentile is between 45 and 50 minutes. To find the exact value, we can use linear interpolation.

First, we find the position of the 40th percentile in relation to the cumulative frequency of 45 minutes (which is 25). The percentile lies in the range between the cumulative frequencies of 45 and 50 minutes, which correspond to positions 25 and 45 in the data set. The 40th percentile is 15% of the way from position 25 to position 45. Therefore, the position of the 40th percentile is:

25 + 0.15(45 - 25) = 30

This means that the 40th percentile corresponds to the time taken by the 30th finisher in the race. We can estimate this time by averaging the times of the 29th and 30th finishers:

(48 + 50) / 2 = 49

Therefore, the 40th percentile is 49 minutes.

Interpretation: The 40th percentile tells us that 40% of the finishers completed the race in 49 minutes or less, while 60% took longer than 49 minutes to complete the race.

give thanks po! and rate5*! your welcome!