I'm working on a statistics project and need to evaluate the expected value using hypergeometric distribution. I am unsure which variable to assign with value in the probability and expected values for the following data: "you work for a manufacturer who receives regular supplies from a supplier, the current acceptance sampling scheme involves sampling 20 units, if more than 2 units are defective the lot is rejected.Assumptions are that the lot size is always 500 and that 4% of units produced by the supplier are defective." In the simulation fuction for the current scheme we are evaluating 1000 shipments loads. Then asked to calculate fraction of incoming lots expected rejected and in comparison to simulation results.... I'm really just lloking to what parts I include in my calculation and variable bearing they hold on hypergeometric distribution functions.

haha i googled the question looking for help and found this, i am probably in your same class, is your project due wednesday?

To evaluate the expected value using hypergeometric distribution in this scenario, you need to consider the following variables:

1. Population size (N): The total number of units in the lot. In this case, it is always 500.

2. Number of successes in the population (K): The number of defective units in the lot. Given that 4% of units produced by the supplier are defective, you can calculate K as follows: K = 0.04 * N = 0.04 * 500 = 20.

3. Sample size (n): The number of units sampled from the lot. In this case, it is always 20.

4. Number of successes in the sample (k): The number of defective units found in the sample. This variable will range from 0 to 2 because if more than 2 units are defective, the lot is rejected.

The hypergeometric distribution function calculates the probability of getting k defective units in a sample of size n, drawn without replacement from a population of size N with K defective units.

The probability mass function (PMF) for the hypergeometric distribution can be calculated using the following formula:

P(X = k) = (K choose k) * ((N - K) choose (n - k)) / (N choose n)

To calculate the expected value, you will sum up the products of the probability of each outcome (k) and the corresponding value of k.

Expected Value (EV) = Σ(k * P(X = k))

To calculate the fraction of incoming lots expected to be rejected, you divide the expected value (EV) by the sample size (n).

Fraction of expected rejected lots = EV / n

To compare the calculated fraction with the simulation results, you need to perform a simulation where you evaluate 1000 shipment loads using the same acceptance sampling scheme. Then, calculate the fraction of rejected lots in the simulation and compare it with the calculated fraction.

Note: The hypergeometric distribution assumes that the lot to be sampled is randomly selected, and the defective units are equally likely to be selected as non-defective units.