Once a week, Haziq rows his boat from the island where he lives to the mainland. The

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Once a week, Haziq rows his boat from the island where he lives to the mainland. The journey time, X minutes, is normally distributed with mean μ and variance σ2.

a. Given that P(20 ≤ X < 30) = 0.32 and that P(X < 20) = 0.63, find the values of μ and σ2.

b. The time taken for Haziq to row back home, Y minutes, is normally distributed and P(Y < 20) = 0.6532.

Given that the variances of X and Y are equal, calculate:

i. The mean time taken by Haziq to row back home

ii. The expected number of days over a period of five years (each of 52 weeks) on which Haziq takes more than 25 minutes to row back home.

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