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8) The probability of tossing a head with a biased coin is 0.62. The coin is tossed 100 times. a) Find the expected number of heads. [3] b) Find the variance of the number of heads. [3] c) A student wishes to use an approximation to estimate the probability that fewer than 70 heads are obtained when the coin is tossed 100 times. To do this, she calculates: 70-62 = $ (1.648) = 0.950 23.56 i) Which of the three values, 70, 62 or 23.56, used by the student is incorrect? Explain why this value is incorrect and state the correct value that she should use. [3] ii) Calculate the probability of obtaining fewer than 70 heads when the coin is tossed 100 times. [3]