Edexcel S1 2018 June — Question 7

Exam BoardEdexcel
ModuleS1 (Statistics 1)
Year2018
SessionJune
TopicNormal Distribution
TypeMixed calculations with boundaries

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 .
  1. Find the percentage of potatoes that Adam grows but cannot sell. The upper quartile of the weight of potatoes sold by Adam is \(q _ { 3 }\)
  2. Find the probability that the weight of a randomly selected potato grown by Adam is more than \(q _ { 3 }\)
  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.
  4. 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 \(q _ { 3 }\)
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