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 $3300, and the average first-year commission for each new account opened is $5100. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account. Determine the equation for computing Gustin’s profit per seminar, given values of the relevant parameters. Round your answers to the nearest dollar. Profit = (New Accounts Opened × $ 5100 ) – $ 3300 What type of random variable is the number of new accounts opened

1) The equation for computing Gustin's profit per seminar is given as follows;

The profit = (The number of Newly Opened Accounts) × Commission - Seminar cost

2) The number of new accounts is a continuous random variable

Step-by-step explanation:

1) The number of individuals that attend each of Gustin's seminar = 25 individuals

The cost of each seminar = $3,300

On average the commission on the first-year for each opened account = $5,100

The probability of opening an account by an attendee of each seminar = 0.01

The profit = Revenue - The cost of each seminar

The revenue = (The number of Newly Opened Accounts) × (Commission on each account)

∴ The revenue = (The number of Newly Opened Accounts) × $5100

Therefore, the equation for finding Gustin's profit per seminar is given as follows;

The profit = (The number of Newly Opened Accounts) × Commission - Seminar cost

The profit = (The number of Newly Opened Accounts) × $5100 - $3,300

The number of Newly Opened Accounts = (The number of attendee) × (The probability of an attendee opening an account)

The number of Newly Opened Accounts = 25 × 0.01 = 0.25

The number of Newly Opened Accounts = 0.25

The profit = 0.25 × $5100 - $3,300

The revenue = 0.25 × $5100 = $1,275

The profit = $1,275 - $5,100 = -$3,825 = ($3,825)

2) The number of Newly Opened Accounts = 0.25 which gives, that Gustin has to conduct 4 seminars to be sure of 1 new account, which represents a probabilistic variable which is the definition of a continuous random variable.

Therefore, the number of new accounts is a continuous random variable.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}