Question

1. if one quart bottles of apple juice have weights that are normally distributed with a mean of 64 ounces and a standard deviation of 3 ounces, what percent of bottles would be expected to have less than 58 ounces?

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 58$, $\mu=64$, and $\sigma = 3$.
Substitute the values into the formula: $z=\frac{58 - 64}{3}=\frac{-6}{3}=- 2$.

Step2: Find the probability from z - table

We need to find $P(Z < - 2)$ for a standard normal distribution. From the standard normal distribution table, the area to the left of $z=-2$ (which represents the probability that a value is less than $x = 58$) is 0.0228 or 2.28%.

Answer:

2.28%