The amount of money spent weekly on cleaning, maintenance, and repairs at a larg

Question

The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean = $629 and standard deviation = $43.

(a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Use 4 decimal places.)

(b) How much should be budgeted for weekly repairs, cleaning, and maintenance so that the probability that the budgeted amount will be exceeded in a given week is only 0.10? (Round to the nearest dollar.)

Explanation / Answer

here from normal distribution z=(X-mean)/std deviation

a) hence P(X>646)=1-P(X<646)=1-P(Z<(646-629)/43)1-P(Z<0.3953)=1-0.6537=0.3463

b)fortop 10% lues at 90 th percentile coresponding to which z=1.28

hence corresponding budgeted amount =mean+z*std deviation =629+1.28*43=684.

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