Question

Suppose that the demand rate is characterized by a normal distribution having a mean of 140 and standard deviation 16. Further, suppose that L(z) is 0.1840. What is the size of the second order that a retailer would make?

Answer 1

To find the size of the second order that a retailer would make, we need to find the z-score that corresponds to the given area under the normal curve. Using the z-score, we can calculate the size of the second order using the mean and standard deviation.

Step-by-step explanation:

To find the size of the second order that a retailer would make, we need to find the z-score that corresponds to the area under the normal curve given. In this case, L(z) is 0.1840, so we need to find the z-score that has an area of 0.8160 to the left of it. Using a calculator, computer, or a probability table for the standard normal distribution, this z-score is approximately 0.8962.

Now, we use the formula z = (x - mean) / standard deviation to find the size of the second order. Rearranging the formula, x = z * standard deviation + mean. Plugging in the values, we have x = 0.8962 * 16 + 140 = 154.3392. Rounding to the nearest whole number, the size of the second order that a retailer would make is 154.