A popular cricket club in Kumasi, has different categories of membership since its formation in 1960 when Ghana became a Republic. The Table below shows the categories of membership, the annual subscription for each category of membership and the probability that a new member will join that category. Category of membership Annual subscription (GHC) Probability FULL 120.00 0.22 SENIOR 80.00 0.28 COUNTRY 75.00 0.12 JUNIOR 30.00 (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)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A popular cricket club in Kumasi, has different categories of
membership since its formation in 1960 when Ghana became a Republic.
The Table below shows the categories of membership,
the annual subscription for each category of membership and the
|
Category of membership |
Annual subscription (GHC) |
Probability |
|
FULL |
120.00 |
0.22 |
|
SENIOR |
80.00 |
0.28 |
|
COUNTRY |
75.00 |
0.12 |
|
JUNIOR |
30.00 |
|
(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)
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