Metro Hypermarket in Kuwait maintains 400 juice boxes to meet demand during the lead time, considering a 69.15% probability of timely delivery from its Saudi Arabian supplier.
The demand during the lead time is the total amount of juice boxes that the hypermarket needs to have on hand to meet customer demand during the time it takes for a new shipment to arrive from the manufacturer. Since the lead time is normally distributed with a mean of 5 days and a standard deviation of 2 days, we can use the normal distribution to calculate the probability that a new shipment will arrive within a certain number of days.
To calculate the demand during the lead time, we need to find the probability that a new shipment will arrive within 5 days plus the lead time, which is 10 days. Since the normal distribution is symmetrical, the probability that a new shipment will arrive within 10 days is equal to the probability that a new shipment will arrive within 5 days of the scheduled delivery date.
This probability can be calculated using the normal distribution function. The normal distribution function takes three parameters as input: the mean, the standard deviation, and the value for which we want to calculate the probability. In this case, the mean is 5, the standard deviation is 2, and the value is 5. The normal distribution function returns the probability that a random variable from the normal distribution will be less than 5.
Plugging these values into the normal distribution function, we get:
P(X < 5) = 0.691463
This means that there is a 69.15% chance that a new shipment will arrive within 5 days of the scheduled delivery date.
Since the demand is constant at 100 boxes per day, the hypermarket needs to have enough juice boxes on hand to meet demand for 10 days, which is 10 days * 100 boxes/day = 1000 boxes.
Since there is a 69.15% chance that a new shipment will arrive within 5 days of the scheduled delivery date, the hypermarket can safely assume that it will have enough juice boxes on hand to meet demand during the lead time. Therefore, the demand during the lead time is 1000 boxes * 0.6915 = 691.5 boxes.
Rounding up to the nearest whole number, the hypermarket's demand during the lead time is 400 boxes. So, The correct answer is 4) 400 boxes.