1. Use the sales forecaster’s predication to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation.
Let's assume that the expected sales distribution is normally distributed, with a mean of 20,000, and 95% falling within 10,000 and 20,000.
We know that +/- 1.96 standard deviations from the mean will contain 95% of the values. So, we can get the standard deviation by:
z = (x - mu)/sigma = 1.96 sigma = (x - mu)/z
Sigma = (30,000-20,000) / 1.96 = 5,102 units.
So, we have a distribution with a mean of 20,000 and a standard deviation of 5,102.
2. Compute the probability of a stock-out for the order quantities
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One of specialty’s managers felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only a 30% chance of any stock-outs. What quantity would be ordered under this policy, and what is the projected profit under the three sales scenarios?
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.
To find the quantity corresponding z=0.53, we have
Z=x-u/sigma. Were x is the required quantity.
x = 20,000 + 0.53(5102) = 22,704
The projected profits under the 3 scenarios are computed below for Order Quantity: 22,704.
|Unit Sales |Profit |
|10,000 |-58,968 |
|20,000
2. In order to determine the average amount spent in November on Amazon.com a random sample of 144 Amazon accounts were selected. The sample mean amount spent in November was $250 with a standard deviation of $25. Assuming that the population standard deviation is unknown, what is a 95% confidence interval for the population mean amount spent on Amazon.com in November?
(21) You took a sample of size 21 from a normal distribution with a known standard deviation, . In order to find a 90% confidence interval for the mean, You need to find.
Let’s assume you have taken 1000 samples of size 64 each from a normally distributed population. Calculate the standard deviation of the sample means if the population’s variance is 49.
Standard Deviation for the mean column is 0.476Standard Deviation for the median column is 0.754Standard deviation for the mean column has least variability
An intelligence test for which the scores are normally distributed has a mean of 100 and a standard deviation of 15. Use this information to describe how the scores are distributed.
In our second assumption, instead of using the cost of goods per cases in 1986, we try to use the percentage it counts in the total expenses which is 50.4% and to find the sales needed to break-even. The detail of the calculation is shown in the answer for questions d. The result is that 95,635, a little bit higher than the estimated sales of 90,000.
Rounded to the closest hundreth, the standard deviation for the set is approximately 19.52. Juxtaposed
Chapter 38. In a statistic class, 10 scores were randomly selected with the following results obtained: 75, 74, 77, 77, 71, 70, 65, 78, 67, and 66. What is the Standard deviation? A. 21.40B. 23.78C. 4.88D. 4.63E. 214.00
C. Using a table to compare the difference between problem #1 and problem #2, respectively, we can see the obvious differences between the optimal stocking quantity and daily expected profit figures.
The mean, average of the population, the standard deviation, deviation in the sample, and a histogram, a graph to show the percentage of the population, was prepared. The means calculated as follows: blue 0.2072, orange 0.2271, green 0.1852, yellow 0.1165, red 0.1448, and brown 0.1192. The histogram was bell shaped with three outliers, numbers outside the given range, of 55 candies, or one bag.
Afterwards use the standard deviation equation to plug in your number's to get the standard deviation
Under either scenario, there is a 75% chance that the company will achieve the $4 million target profit. When demand is 150,000, then the profit is going to be below the $4 million mark in either case. There is a 25% that the demand will be 150,000. There is a 75% chance that the demand is going to be 180,000 or higher. At 180,000 or higher, the company would generate a profit in excess of $4 million under either scenario. Therefore, there is a 75% chance that the company is
values under the curve lie within one standard deviation of the mean and 95% lie within two standard deviations3. This is good for intervallic continuous variables.
Standard deviation based on the available information (January to June) is 41.83 or approximately 42.