Suppose that coffee sales at the Daily Grind are normally distributed with a mean of 225 cups sold each day and a standard deviation of 35 cups.Baristas at the Daily Grind receive a bonus if sales exceed 300 cups.What is the probability that the baristas will receive a bonus on any given day?
A)98.3%
B)48.3%
C)2.1%
D)1.6%
E)1.0%

Question

Quizplus · Accepted Answer

To find the probability that sales exceed 300 cups, we calculate the Z-score for 300 cups using the formula Z = (X - μ) / σ, where X is the value of interest (300 cups), μ is the mean (225 cups), and σ is the standard deviation (35 cups). This gives us Z = (300 - 225) / 35 = 75 / 35 ≈ 2.14. Looking up a Z-score of 2.14 in a standard normal distribution table or using a calculator, we find that the area to the left of Z = 2.14 is approximately 0.9836, meaning the area to the right (the probability of selling more than 300 cups) is 1 - 0.9836 = 0.0164 or 1.6%.

Suppose That Coffee Sales at the Daily Grind Are Normally