Question! G X is the random variable such that X - B(n, p), E(X) = 4.8 and Var(X) = 2.88. Find the values of n and p. The probability of obtaining a head when a biased coin is tossed is p, where p < . An experiment consists of tossing the coin 20 times and recording the number of heads. In a large number of experiments the variance of the number of heads is found to be 4.2. a Estimate the value of p. b Hence estimate the probability that exactly 7 heads are recorded during a particular experiment. C The probability that a salesman gets a reply when he knocks on the door of a house is 0.65. . Find the probability that in a street of 10 houses he receives: i exactly 5 replies ii at least 5 replies. Di How many houses should he visit such that the random variable X = 'number of replies' has a mean of 78? ii What is the variance in this case?

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