Final answer:
At least 77 percent of the apples will contain at least 2.36 ounces of juice, as calculated using the given mean, standard deviation, and the corresponding z-score for the 77th percentile.
Step-by-step explanation:
We are given that the amount of juice obtained from apples is normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce.
To find the amount of juice that at least 77 percent of the apples will contain, we need to determine the z-score that corresponds to the 77th percentile of a standard normal distribution and then use the mean and standard deviation to find the specific value.
Firstly, using a standard normal distribution z-table or percentile calculator, we find the z-score that corresponds to the 77th percentile, which is approximately 0.74. Next, we use the formula for transforming a z-score into an X value:
X = μ + zσ
Where X is the value we want to find (the amount of juice), μ is the mean (2.25 ounces), and σ is the standard deviation (0.15 ounce).
Plugging in the values, we get:
X = 2.25 + 0.74(0.15)
X = 2.25 + 0.111 = 2.361
So, at least 77 percent of the apples will contain at least 2.36 ounces of juice. The closest answer choice is c. 2.36.