Question

1. according to the graph above, what is the median weight of a pumpkin? lbs
2. according to the graph above, what percentage of the data falls within two standard deviations of the mean? %
3. according to the graph above, what percentage of the pumpkins weigh between 35 lb and 55 lb? %
4. according to the graph above, what percentage of pumpkins weigh between 25 lb and 40 lb? %
5. according to the graph above, what percentage of pumpkins weight falls between 1 deviation of the mean? %

Explanation:

Step1: Recall property of normal - distribution

In a normal - distribution, the mean, median, and mode are equal. The mean is at 40 lbs, so the median is also 40 lbs.

Step2: Calculate percentage within two standard deviations

The percentage of data within two standard deviations of the mean is \(13.5\%+34\% + 34\%+13.5\%=95\%\).

Step3: Calculate percentage between 35 lb and 55 lb

The percentage between 35 lb and 40 lb is 34%, and between 40 lb and 55 lb is \(34\% + 13.5\%+2.35\% = 49.85\%\). So the total percentage between 35 lb and 55 lb is \(34\%+49.85\%=83.85\%\).

Step4: Calculate percentage between 25 lb and 40 lb

The percentage between 25 lb and 30 lb is 2.35%, between 30 lb and 35 lb is 13.5%, and between 35 lb and 40 lb is 34%. So the total percentage is \(2.35\%+13.5\%+34\% = 49.85\%\).

Step5: Calculate percentage within one - standard deviation

The percentage within one - standard deviation of the mean is \(34\%+34\% = 68\%\).

Answer:

1. 40
2. 95
3. 83.85
4. 49.85
5. 68