12 The weekly takings at three cinemas are modelled as independent normally distributed random variables with means and standard deviations as shown in the table, in $. Mean Standard deviation Cinema...

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Extracted text: 12 The weekly takings at three cinemas are modelled as independent normally distributed random variables with means and standard deviations as shown in the table, in $. Mean Standard deviation Cinema A 6000 400 Cinema B 9000 800 Cinema C 5100 180 (i) Find the probability that the weekly takings at cinema A will be less than those at cinema C. (ii) Find the probability that the weekly takings at cinema B will be at least twice those at cinema C. (iii) The parent company receives a weekly levy consisting of 12% of the weekly takings at cinema A, 20% of those at cinema B and 8% of those at cinema C. Find the probability that this levy exceeds $3000 in any given week. Hence find the probability that in a 4-week period the weekly levy exceeds $3000 at least twice.


Extracted text: 12 (i) 0.0202 (ii) 0.0856 (iii) 0.3338, 0.4082