Question

(Percentile) 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?

Answer 1

Answer: 77% of the apples will contain at least 2.36 ounces of juice.

Step-by-step explanation:

Since the amount of juice squeezed from each of these apples is approximately normally distributed,

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

z = (x - µ)/σ

Where

x = the amount of juice squeezed in ounces.

µ = mean

σ = standard deviation

From the information given,

µ = 2.25 ounces

σ = 0.15 ounce

Looking at the normal distribution table, the z score corresponding 77%(77/100 = 0.77) is 0.74

Therefore, the number of ounces of juice, x will be

0.74 = (x - 2.25)/0.15

Cross multiplying, it becomes

x - 2.25 = 0.74 × 0.15

x - 2.25 = 0.111

x = 0.111 + 2.25

x = 2.36