The times taken by 15-year-olds to solve a certain puzzle are normally distributed with mean and

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The times taken by 15-year-olds to solve a certain puzzle are normally distributed with mean μ and standard deviation 7.42 minutes.

a. Find the value of μ, given that three-quarters of all 15-year-olds take over 20 minutes to solve the puzzle.

b. Calculate an estimate of the value of n, given that 250 children in a random sample of n 15-year-olds fail to solve the puzzle in less than 30 minutes.

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