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 u and variance o?. a Given that P(20< X < 30) = 0.32 and that P(X < 20) = 0.63, find the values of u and o². 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 pminut
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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