The probability of obtaining heads on a biased coin is 0.4. The coin is tossed 600 times. Write down the mean number of heads and the standard deviation of the number of heads.

The distribution of heads on a biased coin will be binomial - there are only two possible outcomes for a given throw (disregarding the coin standing upright after a toss). Thus X ~ B(600, 0.4) - where X is the number of thrown heads. Obtaining a mean for a binomial distribution requires us to simply multiply the number of trails (in our case 600) by the probability of success (in our case 0.4) - leading us to a mean of 600*0.4 = 240.

The standard deviation is the square root of the trials, chance the trial is successful and the chance that the trial is unsuccessful. (Standard deviation is also the square root of variance). Substituting: sqr(6000.40.6) = sqr(240*0.6) = sqr(144) = 12.