Final answer:
a. The probability of making exactly 4 sales in 2 hours is 0.0096.
b. The probability of making 0 sales in 2 hours is 0.49.
c. The probability of making exactly 2 sales in 2 hours is 0.36.
d. The mean number of sales in the 2 hour period is 3.6.
Step-by-step explanation:
a. To find the probability of making exactly 4 sales in 2 hours, we can use the binomial probability formula. Let's denote a success (making a sale) as S and a failure (not making a sale) as F.
The probability of making a sale in one hour is 30%, so the probability of making a sale in 2 hours is 30% x 2 = 60% or 0.6. Using the binomial probability formula, the probability of making exactly 4 sales in 2 hours is:
- P(X = 4) = (2 choose 4) * (0.6)^4 * (0.4)^2
= (2!/4!(2-4)!) * (0.6)^4 * (0.4)^2
= 0.6^4 * 0.4^2 / (4*3*2*1)
= 0.1296 * 0.16 / 24
= 0.0096
b. The probability of making 0 sales in 2 hours can be found using the complement rule. The complement of making a sale is not making a sale.
The probability of not making a sale in one hour is 1 - 0.3 = 0.7. Therefore, the probability of not making a sale in 2 hours is 0.7^2 = 0.49 or 49%.
c. To find the probability of making exactly 2 sales in 2 hours, we can again use the binomial probability formula.
The probability of making 2 sales in 2 hours is:
- P(X = 2) = (2 choose 2) * (0.6)^2 * (0.4)^0
= 1 * 0.6^2 * 1
= 0.36
d. The mean number of sales in the 2 hour period can be found using the expected value formula for a binomial distribution.
For each hour, the expected number of sales is given by the formula E[X] = n * p, where n is the number of trials (phone calls) and p is the probability of success (making a sale).
In this case, for 2 hours, the expected number of sales is:
- E[X] = 6 * 2 * 0.3
= 3.6 sales