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 μ = $617 and standard deviation σ = $42. (a) If $646 is budgeted for next week, what is the probability that the actual costs will exceed the budgeted amount? (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (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 0.16? (Round your answer to the nearest dollar.) $

Answer 1

a)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	617
std deviation   =σ=	42.0000

probability that the actual costs will exceed the budgeted amount

probability =

P(X>646)

=

P(Z>0.69)=

1-P(Z<0.69)=

1-0.7549=

0.2451

b)

for top 16 percent will fall at 84th percentile:

for 84th percentile critical value of z=		0.99
therefore corresponding value=mean+z*std deviation=			658.6~   $659