use technology or a z - score table to answer the question. the weights of boxes of rice produced at a…

use technology or a z - score table to answer the question. the weights of boxes of rice produced at a factory are normally distributed with a mean of 24 ounces and a standard deviation of 1.3 ounces. consider a shipment of 1200 boxes of rice. how many of the boxes will weigh 25 ounces or less? 192 265 935 1008

use technology or a z - score table to answer the question. the weights of boxes of rice produced at a factory are normally distributed with a mean of 24 ounces and a standard deviation of 1.3 ounces. consider a shipment of 1200 boxes of rice. how many of the boxes will weigh 25 ounces or less? 192 265 935 1008

Answer

Explanation:

Step1: Calculate the z - score

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $x = 25$ (the value we are interested in), $\mu=24$ (the mean), and $\sigma = 1.3$ (the standard deviation). $z=\frac{25 - 24}{1.3}=\frac{1}{1.3}\approx0.77$

Step2: Find the cumulative probability

Using a z - score table, the cumulative probability $P(Z\leq0.77)$ is approximately $0.7794$.

Step3: Calculate the number of boxes

We have a shipment of $n = 1200$ boxes. The number of boxes that weigh 25 ounces or less is $n\times P(Z\leq0.77)$. $1200\times0.7794 = 935.28\approx935$

Answer:

935