As a manufacturer of a flu vaccine, you must decide how many doses of vaccinations to make. You know the following
probability distribution describes the distribution of demand for vaccination: there is a chance demand will be 10 million, a
chance that demand will be 14 million claim, a chance that demand will be 19 million, and otherwise, demand will be
24 million. What is the expected value of demand for vaccinations? (please express your answer in millions and use 2 decimal
places, eg, if your answer is then please write that as 11.560 )

Ask by Herrera Willis. in the United States

Jan 24,2025

Question

As a manufacturer of a flu vaccine, you must decide how many doses of vaccinations to make. You know the following
probability distribution describes the distribution of demand for vaccination: there is a chance demand will be 10 million, a
chance that demand will be 14 million claim, a chance that demand will be 19 million, and otherwise, demand will be
24 million. What is the expected value of demand for vaccinations? (please express your answer in millions and use 2 decimal
places, eg, if your answer is then please write that as 11.560 )

Ask by Herrera Willis. in the United States

Jan 24,2025

UpStudy AI · Accepted Answer

To calculate the **expected value of demand** for vaccinations, we'll use the formula:

$$
E[X] = \sum (\text{Probability} \times \text{Demand})
$$

Given the demand probabilities:

- **10 million** doses with a **42%** probability.
- **14 million** doses with a **20%** probability.
- **19 million** doses with a **17%** probability.
- **24 million** doses with the remaining probability.

First, determine the probability for the 24 million demand:

$$
\text{Total given probability} = 42\% + 20\% + 17\% = 79\%
$$
$$
\text{Probability for 24 million} = 100\% - 79\% = 21\%
$$

Now, calculate the expected value:

$$
E[X] = (0.42 \times 10) + (0.20 \times 14) + (0.17 \times 19) + (0.21 \times 24)
$$
$$
E[X] = 4.2 + 2.8 + 3.23 + 5.04 = 15.27 \text{ million}
$$

**Answer:**  
15.27
The expected demand for vaccinations is **15.27 million** doses.

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