44. (Class Exercise) The previous exercise assumes the coin is balanced. Suppose instead that the probability of a head equals 75 and the probability of a tail equals .25

a) Construct the probability distribution of the outcome of a single flip, and calculate its mean.

b) Each student in the class should sinulate the results of flipping this coin ten times by selecting ten two-digit numbers from the randon number table; a number between 00 and 74 represents a head and a nuinber between 75 and 99 represents a tail Again, construct a plot of the sample proportions, which is an empinical approximation for the true sampling distribution. Compute the mean and standard deviation of the sample proportion values Report the theoretical value for the mean of the samphng distribution. (From Problem 4.55(c), the theoretical standard deviation is .137)