A salesperson contacts eight potential customers per day. From past experience, we know that the probability of a potentail customer making a purchase is 0.10.
a) What is the probability the salesperson will make at least two sales in a day?
-Do you use binomial formula for this question, the answer i got is 0.1869, am i correct?
b) What percentage of days will the salesperson not make a sale?
c) What is the expected number of sales per day?
a) Yes, use the binomial formula and calculate 1 - P(0) - P(1).
I get 1 - 0.4305 + 0.3826 = 0.1869
Congratulations
b) That would be P(0). Use the binomial formula again. I get 43.05%
c) The expected numnber of sales is
8* 0.1 = 0.8.
For a shortcut, use this site:
http://www.ciphersbyritter.com/JAVASCRP/BINOMPOI.HTM#Binomial
but for b) it is asking what percentage of days will the salesperson not make a sale, not what is the probability the salesperson will not make a sale in a day. These are two different questions right, or did i just misunderstood the question?
Yes, you are correct. The question is asking for the percentage of days that the salesperson will not make a sale. To calculate this, you need to use the binomial formula to calculate the probability of not making a sale in a day, and then convert that probability to a percentage.
You are correct, the question is asking for the percentage of days the salesperson will not make a sale, not just the probability. To find the percentage, you can multiply the probability by 100.
b) The percentage of days the salesperson will not make a sale is calculated as P(0) * 100.
Using the binomial formula, P(0) = (8 choose 0) * (0.10^0) * (0.90^8) = 0.4305.
So the percentage of days the salesperson will not make a sale is 0.4305 * 100 = 43.05%.
You are correct, there is a distinction between the probability of not making a sale in a day and the percentage of days that the salesperson will not make a sale.
To answer question b) What percentage of days will the salesperson not make a sale?, you need to calculate the probability of not making a sale in a day, and then convert it to a percentage.
The probability of not making a sale in a day can be calculated using the binomial formula as P(0). Given that the probability of making a sale is 0.10, the probability of not making a sale is 1 - 0.10 = 0.90.
To find the percentage, you multiply the probability by 100. So, the percentage of days that the salesperson will not make a sale is 0.90 * 100 = 90%.
Therefore, the salesperson will not make a sale on approximately 90% of the days.