News Vendor Model Explanation

As discussed in the previous section, a normal distribution has particular characteristics it conforms to. i.e.

The area under the curve to the left of the unknown quantity must be 0.7 (70%). So, we must first find the z value that cuts off an area of 0.7 in the left tail of standard normal distribution. Using the cumulative probability table, we see that z=0.53.

You work in marketing for a company that produces work boots. Quality control has sent you a memo detailing the length of time before the boots wear out under heavy use. They find that the boots wear out in an average of 208 days, but the exact amount of time varies, following a normal distribution with a standard

(a) Then mean of the sample and the value of Z with an area of 10% in right tail.

9. Assume the weight, W, of a randomly selected adult has a normal distribution with a mean

First we look for the area of both by doing “2nd ,Vars, NORMALCDF” and inputting “-1000, “Z,” 0, 1 then find the difference between both.

18. Suppose that the scores of architects on a particular creativity test are normally distributed. Using a normal curve table, what percentage of architects have Z scores:

standard deviation standardized value rescaling z-score normal model parameter statistic standard Normal model 68-95-99.7 Rule normal probability plot

13. Sunglass Hut purchases a pair of Tiffany sunglasses from a wholesaler for $180 and sells it for $300. If the wholesaler increases its price by 20%, to the nearest dollar, what should Sunglass Hut charge in order to maintain the same percent margin?

In order for you to understand how I did this, I will explain that a z-score gives you a way to compare different sets of data using their standard deviations and averages. In statistics, standard deviation is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A standard deviation close to zero tells you the data points are close to the mean or average. Having a high standard deviation shows data points are spread out over a wider range of values. If x is a data point in a normal distribution, then the equation for the z-score of x is x equals x minus the average all divided by the standard deviation. Normal distribution is just a function that represents the distribution of many random variables as a symmetrical bell-shaped graph.

The number of cell phone minutes used by high school seniors follows a normal distribution with a mean of 500 and a standard deviation of 50. What is the probability that a student uses more than 350 minutes?

The rate of demand is known and normally distributed which have been proved by the normality test presented above.

30. The manager of the local National Video Store sells videocassette recorders at discount prices. If the store does not have a video recorder in stock when a customer wants to buy one, it will lose the sale because the customer will purchase a recorder from one of the many local competitors. The problem is that the cost of renting warehouse space to keep enough recorders in inventory to meet all demand is excessively high. The manager has determined that if 90% of customer demand for recorders can be met, then the combined cost of lost sales and inventory will be minimized. The manager has estimated that monthly demand for recorders is normally distributed, with a mean of 180 recorders and a standard deviation of 60. Determine the number of recorders the manager should order each month to meet 90% of customer demand.

right-hand side and divide both sides by P, we can rewrite this equation and find the price-cost

Since the expected demand is 2000, thus, the mean µ is 2000. Through Excel, we get the z value given a 95% probability is 1.96. Thus, we have: z= (x-µ)/ σ=(30000-20000)/