in a certain orchard, the number of apples (a) on a tree is normally distributed with a mean of 300 apples…

Explanation:

Step1: Recall the 68 - 95 - 99.7 rule

The 68 - 95 - 99.7 rule for a normal distribution states that about 68% of the data lies within 1 standard - deviation of the mean ($\mu\pm\sigma$), about 95% lies within 2 standard - deviations of the mean ($\mu\pm2\sigma$), and about 99.7% lies within 3 standard - deviations of the mean ($\mu\pm3\sigma$). Here, $\mu = 300$ and $\sigma=30$.

Step2: Determine the number of standard - deviations from the mean

The value 240 is $\frac{300 - 240}{30}=2$ standard - deviations below the mean ($\mu - 2\sigma$), and 300 is the mean ($\mu$).

Step3: Use the symmetry of the normal distribution

Since the normal distribution is symmetric about the mean, the percentage of data between $\mu - 2\sigma$ and $\mu$ is half of the percentage of data between $\mu - 2\sigma$ and $\mu + 2\sigma$. The percentage of data between $\mu - 2\sigma$ and $\mu+2\sigma$ is 95%. So the percentage of data between $\mu - 2\sigma$ and $\mu$ is $\frac{95%}{2}=47.5%$.

Answer:

47.5%