An apple juice producer buys all his apples from a conglomerate of apple growers in one northwest state.The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. 77% of the apples will contain at least how many ounces of juice?
A)2.12
B)2.38
C)2.36
D)2.14

Question

Quizplus · Accepted Answer

To find the amount of juice that 77% of apples will contain at least, we need to find the 23rd percentile (since 100% - 77% = 23%) of the normal distribution with mean 2.25 and standard deviation 0.15. Using the Z-table, the Z-score for the 23rd percentile is approximately -0.74. Using the formula X = μ + Zσ, we calculate X = 2.25 + (-0.74)(0.15) ≈ 2.14.

An Apple Juice Producer Buys All His Apples from a Conglomerate