You have been hired by The Wolf of Wall Street to call peopl

You have been hired by The Wolf of Wall Street to call people and convince them to buy stocks. If you do not sign up at least two customers a day, you will be fired that day. (On average, your colleagues sign up three customers a day.) Each call you make has a probability of 0.10 that the customer will sign up with your firm. (The probability that a person will sign up is independent).

If you make 50 calls today, what is the probability that you will not be fired?

If you make 50 calls today, how many customers do you expect to sign up?

2.X is a uniformly distributed continuous variable, whose lowest possible value is 2 and whose standard deviation is ?3. What is the expected value of X?

Solution

This is a binomial distribution.

Number of trials, n = 50

Probability of success = .10

To find the probability of not getting fired:

It\'s actually easier to first find the probability of getting fired.

You will get fired if you only sign up 0 or 1 persons.

So we want to find the probability of signing up 0 or 1 persons.

We\'ll use the binomial probability formula for this:

P(X = x) = nCx*P^x*(1-p)^(n-x)

P(X = 0) = 50C0*.1^(0)*(1-.1)^(50-0)

= 50C0*.1^0*.9^50 = .005154

P(X = 1) = 50C1*.1^(1)*(1-.1)^(50-1)

= 50C1*.1^1*.9^49 = .028632

P(X equals 0 or 1) = .005154 + .028632 = .033786

So your probability of being fired is .033786

and your probability of not being fired is 1 - .0033786 = 0.9662

answer: 0.9662

The expected number of customers:

This is the mean.

The mean for the binomial distribution is n*p

n*p = 50*.1 = 5

answer: You expect to sign up 5 people.