Answer to Question #235332 in Statistics and Probability for Hastings Mambwe

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?

[6 marks]

b) A bank has 175 000 credit card holders. During one month the average

amount spent by each card holder totalled $192,50 with a standard deviation

of $60,20. Assuming a normal distribution, determine the number of card holders

who spent more than $250.

Answer 1

a) The average demand is 8 motors per week.

Demand~pois(8)

For a poisson distribution,;

$P(X=x)=\frac{e^{-\lambda} \lambda^x}{x!}$

$P(X\le n)\ge0.95$

$\sum_{x=0}^n \frac{e^{-8}8^x}{x!}\ge0.95$

$\sum_{x=0}^n \frac{8^x}{x!}\ge \frac{0.95}{e^{-8}}$

$\sum_{x=0}^n \frac{8^x}{x!}\ge 2831.91$

from the series n=13

The minimum number of motors should be 13.

b) n=175000

$\ { \mu=192.5 , \sigma=60.20}$

X~$N(\mu, \sigma^2)$

P(X>250)=P(z>$\frac{250-192.50}{60.20}$ )

=P(z>0.96)

=0.1685 from the z tables.

Number of credit card holders=175000*0.1685

=29488