Question

The weekly demand for a product follows a normal distribution with mean 1000 and standard deviation 200. The current inventory is 2,200 and no deliveries will be occurring in the next two weeks. What is the probability that the total of the demands in the next two weeks exceeds 2,200?

Answer 1

Answer:

$P(Y_1+Y_2)=0.0073$

Step-by-step explanation:

Let $Y_i$ be a random variable, defined as weekly demand, with the parameters$\mu=1000 \ and\ \sigma=200$. Therefore, the probability that total demands in the next two weeks, $Y_1 \ and \ Y_2$, exceeds 2,200 is denoted as$P(Y_1+Y_2)$

$P(Y_1+Y_2)=P(Y_1+Y_2>2200)\\=P(Y_1+Y_2-\mu_1-\mu_2>2200-\mu_1-\mu_2)\\=P(\frac{Y_1+Y_2-\mu_1-\mu_2}{\sqrt(\sigma_1^2+\sigma_2^2}>\frac{2200-\mu_1-\mu_2}{\sqrt(\sigma_1^2+\sigma_2^2})\\=P(z>\frac{2200-2000}{\sqrt(40000+40000})\\=P (z >2.24)\\=1-P(z >2.24)=1-0.9927=0.0073$

P(Y1+Y2)=0.0073