7. A farmer uses many identical containers to store four different types of grain: wheat, corn, einkorn and emmer.
- The mass \(W\), in kg , of wheat stored in each individual container is normally distributed with mean \(\mu\) and standard deviation \(0 \cdot 6\). Given that, for containers of wheat, \(10 \%\) store less than 19 kg , find the value of \(\mu\).
The mass \(X\), in kg , of corn stored in each individual container is normally distributed with mean \(20 \cdot 1\) and standard deviation \(1 \cdot 2\). - Find the probability that the mean mass of corn in a random sample of 8 containers of corn will be greater than 20 kg .
The mass \(Y\), in kg, of einkorn stored in each individual container is normally distributed with mean \(22 \cdot 2\) and standard deviation \(1 \cdot 5\).
The farmer and his wife need to move two identical wheelbarrows, one of which is loaded with 3 containers of corn, and the other of which is loaded with 3 containers of einkorn. They agree that the farmer's wife will move the heavier wheelbarrow. - Calculate the probability that the farmer's wife will move
- the einkorn,
- the corn.
- The mass \(E\), in kg , of emmer stored in each individual container is normally distributed with mean \(10 \cdot 5\) and standard deviation \(\sigma\). The farmer's son tries to calculate the probability that the mass of corn in a single container will be more than three times the mass of emmer in a single container. He obtains an answer of 0.35208 .
- Find the value of \(\sigma\) that the farmer's son used.
- Explain why the value of \(\sigma\) that he used is unreasonable.
Additional page, if required. Write the question number(s) in the left-hand margin.
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