1. (a) The Monthly expenditure of family is nomally distributed with mean riyals 100 and variance Riyals 64. Evaluate the probability that the expenditure of a family is ) between 110.5 and 125.75, (ii) at most 93.5. (b) P(Z< K) = 0.45. Evaluate K. II. Listed is data on profit and market capitalization for a sample of 5 different firms: Market 20 40 55 18 40 (X) Profit 30 22 18 35 (Y) A. Find the Karl Person's coefficient of corelation B. Find an estimate of profit when market capitalization is 30

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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!