Question

There is a 20% chance that the number of employees in a

Modesto store will increase by 300. There is a 70% chance that
the increase will be 400 employees. There is a 10% chance that
the number of employees will decrease by 500. Determine the
expected gain or loss of employees for the next year.
Show all calculations for full credit and submit a picture of your
work by the deadline.

Answer 1

Let X be the random variable representing the change in the number of employees for the next year. We can find the expected value of X as:

E(X) = (probability of gain) * (gain) + (probability of loss) * (loss)

We know that the store will increase by 300 employees, and there is a 70% chance that the increase will be 400 employees. Therefore, the probability of gaining 400 employees is 0.7, and the gain is 400.

We also know that there is a 10% chance that the number of employees will decrease by 500. Therefore, the probability of losing 500 employees is 0.1, and the loss is -500.

Substituting these values into the formula for the expected value, we get:

E(X) = (0.7)(400) + (0.1)(-500)

E(X) = 280 - 50

E(X) = 230

Therefore, the expected gain or loss of employees for the next year is 230 employees. We expect the store to gain 230 employees on average.