The time, T minutes, taken to complete a jigsaw puzzle can be modelled by a normal distribution with mean μ and standard deviation 8.6. It is found that 30% of times taken to complete the jigsaw puzzle are longer than 36.8 minutes a) By stating and solving an appropriate equation, show, correct to two decimal places, that μ = 32.29 Use μ = 32.29 in the remainder of the question. b) Find the 86th percentile time to complete the jigsaw puzzle. c) Find the probability that a randomly chosen person will take more than 30 minutes to complete the jigsaw puzzle. Six randomly chosen people complete the jigsaw puzzle.
The time, T minutes, taken to complete a jigsaw puzzle can be modelled by a
normal distribution with mean μ and standard deviation 8.6.
It is found that 30% of times taken to complete the jigsaw puzzle are longer than
36.8 minutes
a) By stating and solving an appropriate equation, show, correct to two
decimal places, that μ = 32.29
Use μ = 32.29 in the remainder of the question.
b) Find the 86th percentile time to complete the jigsaw puzzle.
c) Find the probability that a randomly chosen person will take more than 30 minutes to complete the jigsaw puzzle.
Six randomly chosen people complete the jigsaw puzzle.
d) Find the probability that at least five of them will take more than 30 minutes to complete the jigsaw puzzle.
Having spent 25 minutes attempting the jigsaw puzzle, a randomly chosen person had not yet completed the puzzle.
e) Find the probability that this person will take more than 25 minutes to complete the jigsaw puzzle.
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