In: Statistics and Probability
Problem 16-05
To generate leads for new business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3100, and the average first-year commission for each new account opened is $5800. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account.
Simulation Trial | New Accounts |
1 | 0 |
2 | 0 |
3 | 1 |
4 | 0 |
5 | 0 |
6 | 0 |
7 | 0 |
8 | 1 |
9 | 0 |
10 | 2 |
11 | 0 |
12 | 0 |
13 | 0 |
14 | 2 |
15 | 1 |
16 | 0 |
17 | 0 |
18 | 0 |
19 | 1 |
20 | 0 |
21 | 0 |
22 | 0 |
23 | 0 |
24 | 0 |
25 | 0 |
(a)
Profit = (New Accounts Opened × $5800) – $3100
(b)
The number of new accounts opened is a binomial random variable with 25 trials and 0.01 probability of success on a single trial.
(c)
Simulation Trial | New Accounts | Fixed Cost | Commission per new account | Total Commission | Profit |
1 | 0 | 3100 | 5800 | 0 | -3100 |
2 | 0 | 3100 | 5800 | 0 | -3100 |
3 | 1 | 3100 | 5800 | 5800 | 2700 |
4 | 0 | 3100 | 5800 | 0 | -3100 |
5 | 0 | 3100 | 5800 | 0 | -3100 |
6 | 0 | 3100 | 5800 | 0 | -3100 |
7 | 0 | 3100 | 5800 | 0 | -3100 |
8 | 1 | 3100 | 5800 | 5800 | 2700 |
9 | 0 | 3100 | 5800 | 0 | -3100 |
10 | 2 | 3100 | 5800 | 11600 | 8500 |
11 | 0 | 3100 | 5800 | 0 | -3100 |
12 | 0 | 3100 | 5800 | 0 | -3100 |
13 | 0 | 3100 | 5800 | 0 | -3100 |
14 | 2 | 3100 | 5800 | 11600 | 8500 |
15 | 1 | 3100 | 5800 | 5800 | 2700 |
16 | 0 | 3100 | 5800 | 0 | -3100 |
17 | 0 | 3100 | 5800 | 0 | -3100 |
18 | 0 | 3100 | 5800 | 0 | -3100 |
19 | 1 | 3100 | 5800 | 5800 | 2700 |
20 | 0 | 3100 | 5800 | 0 | -3100 |
21 | 0 | 3100 | 5800 | 0 | -3100 |
22 | 0 | 3100 | 5800 | 0 | -3100 |
23 | 0 | 3100 | 5800 | 0 | -3100 |
24 | 0 | 3100 | 5800 | 0 | -3100 |
25 | 0 | 3100 | 5800 | 0 | -3100 |
Average Profit | -1244 |
No of time profit< 0 | 19 |
Probability of loss | 0.76 |
So,
The expected profit from a seminar is $ -1244 and there
is a 0.76 probability of a loss.
Gustin should not conduct the seminars in their current
format.
(d)
The average number of new accounts = n.p (binomial distribution property) where p = 0.01 and 'n' is unknown.
The profit is greater than zero when the commission is greater than the cost. So,
n.p*5800 > 3100
or, n > 3100 / (5800*0.01)
or, n > 53.44
The answer should be 53 attendees and we do not need trial and error for this.