Mathematics (AS & A Level) · Oct / Nov 2023 · Paper 62 · Question 6

A factory makes loaves of bread in batches. One batch of loaves contains X kilograms of dried yeast and Y kilograms of flour, where X and Y have the independent distributions N0.7, 0.022 and N100.0, 3.02 respectively. Dried yeast costs $13.50 per kilogram and flour costs $0.90 per kilogram. For making one batch of bread the total of all other costs is $55. The factory sells each batch of bread for $200. Find the probability that the profit made on one randomly chosen batch of bread is greater than $40. [7] 11

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