7. Posting fees. Weekly postage expenses for your company have a mea of $325 and

Question

7. Posting fees. Weekly postage expenses for your company have a mea of $325 and a standard deviation of $54. Your company has allowed for $350 postage per week in its budget. (a) What is the probability that the average weekly postage expenses for the past 9 months (assume each month has 4 weeks) exceed the budgeted amount of $350? (b) The recent problems with the stock market are affecting your business and you need to reallocate some of your funds, so you'd like to reduce your postage expenses. What is the probability that your postage for the next week will not exceed $330?

Explanation / Answer

Mean of weekly postage charges for the company i.e = 325

Standard of eweekly postage charges for the company i.e = 54

weekly postage expense allowed per week in budget = 350

a)

let us denote average weekly postage charge by y

No of weeks in 9 months = 9*4 = 36 => sample size i.e n = 36

mean of average weekly of postage expense for 9 months i.e mean of y= Mean of weekly postage charges for the company = 325

standard deviation of average weekly of postage expense for 9 months i.e standard deviation of y= /n = 54/36 = 54/6 = 9

z value = (y- mean)/standard deviation

z value y=350 is (350-325)/9 = 2.7777, corresponding p value using z table is 0.9973

so P(Y<=350) = 0.9973

P(Y>350) = 1- 0.9973 = 0.0027

so probability that average weekly of postage expense for 9 months exceed $350 is 0.0027

b)

let us denote weekly postage expense by x

mean of x = 325

standard deviation of x = 54

z value x=330 is (330-325)/54 = 0.0925, corresponding p value using z table is 0.5369

so P(X<=330) = 0.5369

so probability that your postage for the next week will not exceed $330 is 0.5369

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