Question

9. A local fast-food restaurant finds that its daily profit has mean μ =50 dollars and standard deviation σ =100 dollars. If an auditor randomly selects 30 days, what is the probability that the average profit of the 30 days is a loss (i.e., average profit is less than 0)? (4pts)

Answer 1

Here, μ = 50, σ = 18.2574 and x = 0. We need to compute P(X <= 0). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (0 - 50)/18.2574 = -2.74

Therefore,
P(X <= 0) = P(z <= (0 - 50)/18.2574)
= P(z <= -2.74)
= 0.0031