Portion control is one of the biggest problems in the cafeteria industry. For ex
ID: 3155416 • Letter: P
Question
Portion control is one of the biggest problems in the cafeteria industry. For example, if the average amount of mashed potatoes given to a customer is too large, it will damage your profit maigin. Likewise, if the amount is too small, it will damage your customer base. As a recent graduate of U.TA. you were asked to set up a program to periodically estimate the average amount of potatoes served by each server. Y ou decide to ask 4 of your friends to go eat at the cafeteria free and order potatoes. Y ou then sneak the potato servings out of the door and take them to a lab where you measure the amount in each serving resulting in the following data (assumedata is normal). DATA (IN OUNCES): 10,14,12,12 Provide a point estimate for the average amount of potatoes in each serving. mux - x = (10+14+12+12)/4 = 12 Provide a 95% confidence interval estimate for the average amount of potatoes. You would use the t statistic here instead of the z statistic because you estimated the standard deviation from the data, which is the typical case. Note the assumption that the population is normal.Explanation / Answer
Getting the mean, X,
X = Sum(x) / n
Summing the items, Sum(x) = 48
As n = 4
Thus,
X = 12
Setting up tables,
Thus, Sum(x - X)^2 = 8
Thus, as
s^2 = Sum(x - X)^2 / (n - 1)
As n = 4
s^2 = 2.666666667
Thus,
s = 1.632993162 [ANSWER]
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Hi! You can also use technology. One of the easiest ways is to find an online resource that calculates standard deviation. You can also use spreadsheets like the STDEV function in Excel. Thanks!
x x - X (x - X)^2 10 -2 4 14 2 4 12 0 0 12 0 0