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 ? = $615 and standard deviation ? = $38.

(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.)

Answer 1

Calculate the Z-score using the budgeted amount, the mean, and standard deviation, then find the corresponding probability that costs will exceed this budgeted amount based on the standard normal distribution.

Step-by-step explanation:

The student is asking about finding the probability that the actual costs will exceed a budgeted amount for a normally distributed variable representing weekly expenses on cleaning, maintenance, and repairs at a large restaurant. Given the mean ($615) and standard deviation ($38), and the budget for next week being $646, we need to calculate a Z-score for the budgeted amount and then find the corresponding probability from the standard normal distribution table or computational tools like statistical software or a calculator.

To calculate the Z-score, use the formula Z = (X - μ)/σ, where X is the value for which we are finding the probability, μ the mean, and σ the standard deviation. Then, refer to the standard normal distribution table or a calculator to find the probability of the Z-score, which will give us the probability that actual costs exceed the budgeted amount.

The Z-score is calculated as follows: Z = (646 - 615) / 38 = 0.8158. The probability that Z is greater than 0.8158 can be found in a standard normal distribution table or with a calculator to provide the desired answer, which will be rounded to four decimal places as instructed.