Question

"A local bakary has determined a probability distribution for the

number of cheesecakes that they sell in a given day.
X= #sold: 0 5 10 15 20
Probability : 0.26 0.16 0.3 ...? 0.18
What is the probability of selling 15 cheesecakes in a given day?
Give the expected number of cheesecakes sold in a day using the discrete probability
distribution?

Answer 1

The probability of selling 15 cheesecakes is 0.10. The expected number of cheesecakes sold in a day is calculated to be 8.9 using the discrete probability distribution.

Step-by-step explanation:

The probability of selling 15 cheesecakes in a given day is not provided directly in the question. However, we do know that probability distributions must add up to 1. Given the other probabilities for 0, 5, 10, and 20 cheesecakes, we can subtract the sum of those probabilities from 1 to find the missing probability for selling 15 cheesecakes.

To calculate the expected number of cheesecakes sold in a day, we will use the discrete probability distribution. We multiply each number of cheesecakes (X) by its corresponding probability and then sum those products to get the expected value.

Here is the step-by-step calculation:

1. First, sum the known probabilities: 0.26 + 0.16 + 0.3 + 0.18 = 0.90.
2. The missing probability is: 1 - 0.90 = 0.10, so there is a 0.10 probability of selling 15 cheesecakes in a given day.
3. Now calculate the expected value: (0 * 0.26) + (5 * 0.16) + (10 * 0.3) + (15 * 0.10) + (20 * 0.18).
4. The result is: 0 + 0.8 + 3 + 1.5 + 3.6 = 8.9 cheesecakes.

Therefore, the expected number of cheesecakes sold in a day using the discrete probability distribution is 8.9.