If $642 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.)

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 = $605 and standard deviation 𝜎 = $44.

Answer 1

Hi Arylette,

This problem uses the classic introductory statistics equation z= (x - mu)/sigma

x=value you are interested in

mu=mean

sigma=standard deviation

You will need a z-score table, which can easily be found online. To our problem:

x=642

mu=605

sigma=44

z= (642-605)/44

z= 0.84

Now, go to the z table and look up 0.8 in the row and 0.04 in the column.

This gives P=0.7995, but remember that probabilities in the z-table are for less than. We want greater than, so we use the Complement Rule aka the “one minus trick.”

P(Z>0.84)=1-P(Z<0.84)=P(X>642)= 1 - 0.7995 = 0.2005

I hope this helps.