A popular cricket club in Kumasi, has different categories of membership since its formation in 1960 when Ghana became a Republic. The Table on the right hand side shows the categories of membership, the annual subscription for each category of membership and the probability that a new member will join that category. (a) Show that the mean subscription paid by new members is GH 69.20 (b) Find the variance and standard deviation of the subscription paid by new members. (c) As the ground capacity is limited, only 400 new members can be accepted during the coming year. The club is to stage an international match and so expects more than 400 applications for membership. As a result, it was decided that only applications for full membership would be accepted. How many full members would the club need to accept in order to receive more money in subscriptions than would have been provided by 400 members distributed as in the table given above? (d) Give one disadvantage of the decision in part (c). [ Hint: Use Discrete Probability Distribution ] Category Of membership Annual subscription (GH ) Probability FULL 120.00 0.22 SENIOR 80.00 0.28 COUNTRY 75.00 0.12 JUNIOR 30.00 0.38