Cocoa Plant Height
1. The problem asks for the probability that the height of a randomly selected cocoa plant is between 110 cm and 130 cm.
2. To solve this, we need the probability distribution of the cocoa plant heights (e.g., normal distribution parameters: mean $\mu$ and standard deviation $\sigma$).
3. Assuming the height follows a normal distribution $X \sim N(\mu, \sigma^2)$, the probability is $P(110 \leq X \leq 130) = P\left(\frac{110 - \mu}{\sigma} \leq Z \leq \frac{130 - \mu}{\sigma}\right)$ where $Z$ is a standard normal variable.
4. Calculate the z-scores: $z_1 = \frac{110 - \mu}{\sigma}$ and $z_2 = \frac{130 - \mu}{\sigma}$.
5. Use standard normal distribution tables or a calculator to find $P(z_1 \leq Z \leq z_2) = \Phi(z_2) - \Phi(z_1)$ where $\Phi$ is the cumulative distribution function (CDF) of the standard normal.
6. Without specific $\mu$ and $\sigma$ values, the exact probability cannot be computed.
7. If you provide the mean and standard deviation, I can calculate the exact probability.