A farmer harvested 250 potatoes which were grown using Fertiliser X. The cumulative frequency curve below shows the mass distribution of the potatoes.
The farmer only sells potatoes that weigh 56 g and above. Using the curve, find the percentage of potatoes that can be sold.[1]
Complete the grouped frequency table for the mass of the potatoes.
Complete the grouped frequency table.[1]
Find the interval that contains the median mass.[1]
Calculate an estimate of the mean mass.[1]
Calculate an estimate of the standard deviation of the masses.[1]
| Mass (\(m\text{ g}\)) | \(20\leq m<40\) | \(40\leq m<60\) | \(60\leq m<80\) | \(80\leq m<100\) | \(100\leq m<120\) |
|---|
| Frequency | \(35\) | | \(95\) | \(55\) | \(20\) |
Two of the potatoes are selected at random, without replacement. Find the probability that
none has a mass between 60 g and 100 g,[2]
one has a mass less than 60 g and the other has a mass greater than 100 g.[2]
The farmer harvested another 250 potatoes that were grown using Fertiliser Y. The estimated mean mass of this batch of potatoes is 62 g. The estimated standard deviation of the masses is 23 g. Make two comments comparing the mass of the potatoes grown using Fertiliser X and those grown using Fertiliser Y.[2]