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 = $597 and standard deviation σ = $39. (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.)

The probability that the actual costs will exceed the budgeted amount is 0.104.

Step-by-step explanation:

Since 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, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = amount of money spent.

µ = mean

σ = standard deviation

From the information given,

µ = $597

σ = $39

The probability that the actual costs will exceed the budgeted amount($646) is expressed as

P(x > 646) = 1 - P(x ≤ 646)

For x = 646,

z = (646 - 597)/39 = 1.26

Looking at the normal distribution table, the probability corresponding to the z score is 0.896

P(x > 646) = 1 - 0.896

P(x > 646) = 0.104

536

step-by-step explanation: