A salesperson contacts eight potential customers per day. From past experience, we know that the probability of a potential customer making a purchase is .10.a. What is the probability the salesperson will make exactly two sales in a day?b. What is the probability the salesperson will make at least two sales in a day?c. What percentage of days will the salesperson not make a sale?d. What is the expected number of sales per day?

(a) The probability the salesperson will make exactly two sales in a day is 0.1488.

(b) The probability the salesperson will make at least two sales in a day is 0.1869.

(c) The percentage of days the salesperson does not makes a sale is 43.05%.

(d) The expected number of sales per day is 0.80.

Step-by-step explanation:

Let X = number of sales made by the salesperson.

The probability that a potential customer makes a purchase is 0.10.

The salesperson contacts n = 8 potential customers per day.

The random variable X follows a Binomial distribution with parameters n and p.

The probability mass function of X is:

(a)

Compute the probability the salesperson will make exactly two sales in a day as follows:

Thus, the probability the salesperson will make exactly two sales in a day is 0.1488.

(b)

Compute the probability the salesperson will make at least two sales in a day as follows:

P (X ≥ 2) = 1 - P (X < 2)

              = 1 - P (X = 0) - P (X = 1)

Thus, the probability the salesperson will make at least two sales in a day is 0.1869.

(c)

Compute the probability that a salesperson does not makes a sale is:

The percentage of days the salesperson does not makes a sale is,

0.4305 × 100 = 43.05%

Thus, the percentage of days the salesperson does not makes a sale is 43.05%.

(d)

Compute the expected number of sales per day as follows:

Thus, the expected number of sales per day is 0.80.