7. Farmer Adam grows potatoes. The weights of potatoes, in grams, grown by Adam are normally distributed with a mean of 140 g and a standard deviation of 40 g .
Adam cannot sell potatoes with a weight of less than 92 g .
- Find the percentage of potatoes that Adam grows but cannot sell.
The upper quartile of the weight of potatoes sold by Adam is \(q _ { 3 }\)
- Find the probability that the weight of a randomly selected potato grown by Adam is more than \(q _ { 3 }\)
- Find the lower quartile, \(q _ { 1 }\), of the weight of potatoes sold by Adam.
Betty selects a random sample of 3 potatoes sold by Adam.
- Find the probability that one weighs less than \(q _ { 1 }\), one weighs more than \(q _ { 3 }\) and one has a weight between \(q _ { 1 }\) and \(q _ { 3 }\)