Question

16. A cosmetics salesperson, who calls potential customers to sell her products, has determined that 30% of her telephone calls result in a sale. Determine the probability distribution for her next three calls. Calculate the probabilities that the next three calls could result in 0, 1, 2, or 3 sales, respectively.

I dont understand how this is a binomial

Binomial distribution with p = 0.3 and n = 3 P(x = 0) = 0.73 = 0.343 P(x = 1) = 3 · 0.3 · 0.72 = 0.441 P(x = 2) = 3 · 0.32 · 0.7 = 0.189 P(x = 3) = 0.33 = 0.027

I don't understand how this is a binomial distribution ???

One condition of Binomial is Success or failure???

Best,

Nick

Answer 1

In a binomial distribution, there are only two possible outcomes, success and failure. The n trials of the experiment are independent and probability of success remains unchanged from trial to trial.

Here, if the telephone call results in a sale, we view that as a success and failure otherwise.

The outcome of any call is independent of other calls, so each trial is independent.

Also, the probability of success is 0.3 for each trial.

So, all the conditions of a binomial distribution are fulfilled. So, we can view this problem as binomial, with parameters n=3 and p=0.3

  

P(x=0) = 0.7³

= 0.343

P(x=1) = 3*0.3*0.7²

= 0.441

P(x=2) = 3*0.3²*0.7

=0.189

P(x=3) = 0.3³

= 0.027