the weight of oranges growing in an orchard is normally distributed with a mean weight of 7.5 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 $x = 5$: $z_1=\frac{5 - 7.5}{1.5}=\frac{- 2.5}{1.5}\approx - 1.67$. For $x = 7$: $z_2=\frac{7 - 7.5}{1.5}=\frac{-0.5}{1.5}\approx - 0.33$.

Step2: Use the standard normal table

We want to find $P(-1.67<Z<-0.33)$. We know that $P(-1.67<Z<-0.33)=P(Z < - 0.33)-P(Z < - 1.67)$. From the standard - normal table, $P(Z < - 0.33)=0.3707$ and $P(Z < - 1.67)=0.0475$.

Step3: Calculate the probability

$P(-1.67<Z<-0.33)=0.3707 - 0.0475=0.3232$.

Answer:

$32.3%$