Answer to Question #231655 in Statistics and Probability for Jamilah

Question

a) The average demand on a factory store for a certain electric motor is 8 per week.
When the storeman places an order for these motors, delivery takes one week.
If the demand for motors has a Poisson distribution, how low can the storeman
allow his stock to fall before ordering a new supply if he wants to be at least
95% sure of meeting all requirements while waiting for his new supply to arrive?

Answer 1

QUESTION

a) The average demand on a factory store for a certain electric motor is 8 per week.

When the store man places an order for these motors, delivery takes one week.

If the demand for motors has a Poisson distribution, how low can the store man

allow his stock to fall before ordering a new supply if he wants to be at least

95% sure of meeting all requirements while waiting for his new supply to arrive?

SOLUTION

The average demand for the electric motor is 8 vehicles per week.

Meaning x = 8

The demand is therefore distributed in a poison distribution way, where: P(x = k) = (e^-$\lambda$ *$\lambda$^k)/(k!)

P(x ≤ n) ≥ 0.95

Proceed to find the value of n from the above equation that will be the minimum stock required.

(e^-88⁰)/(0!) + (e^-88¹)/(1!) + (e^-88²)/(2!) + ... + (e^-88ⁿ)/(n!) ≥ 0.95

e^-8 (8⁰/0! + 8¹/1! + 8²/2! + ... + 8ⁿ/n!) ≥ 0.95

8⁰/0! + 8¹/1! + 8²/2! + ... + 8ⁿ/n! ≥ 283191009

From the series, the minimum value of n = 13, that meet the 95% demand requirement before another supply reaches the store in one week. So the store man need to have at least 13 electric motors in the store.

ANSWER: 13 Electric motors