the weight of oranges growing in an orchard is normally distributed with a mean weight of 8 oz. and a…

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set. For $x = 9$, $z_1=\frac{9 - 8}{1.5}=\frac{1}{1.5}\approx0.67$. For $x = 10$, $z_2=\frac{10 - 8}{1.5}=\frac{2}{1.5}\approx1.33$.

Step2: Use the standard normal table

We want to find $P(0.67<Z<1.33)$. From the standard - normal table, $P(Z < 1.33)=0.9082$ and $P(Z < 0.67)=0.7486$. Then $P(0.67<Z<1.33)=P(Z < 1.33)-P(Z < 0.67)$. $P(0.67<Z<1.33)=0.9082 - 0.7486=0.1596$.

Step3: Convert to percentage

To convert the probability to a percentage, we multiply by 100. $0.1596\times100 = 15.96%\approx16.0%$.

Answer:

$16.0%$