- A machine squeezes apples to extract their juice. The volume of juice, \(J \mathrm { ml }\), extracted from 1 kg of apples is modelled by a normal distribution with mean \(\mu\) and standard deviation \(\sigma\)
Given that \(\mu = 500\) and \(\sigma = 25\) use standardisation to
- show that \(\mathrm { P } ( J > 510 ) = 0.3446\)
- calculate the value of \(d\) such that \(\mathrm { P } ( J > d ) = 0.9192\)
Zen randomly selects 5 bags each containing 1 kg of apples and records the volume of juice extracted from each bag of apples.
- Calculate the probability that each of the 5 bags of apples produce less than 510 ml of juice.
Following adjustments to the machine, the volume of juice, \(R \mathrm { ml }\), extracted from 1 kg of apples is such that \(\mu = 520\) and \(\sigma = k\)
Given that \(\mathrm { P } ( R < r ) = 0.15\) and \(\mathrm { P } ( R > 3 r - 800 ) = 0.005\)
- find the value of \(r\) and the value of \(k\)