To calculate the probability that the sample proportion is between 0.14 and 0.16, we need to follow these steps:

1. Define the problem and the formula

We know the sampling distribution of the sample proportion is normally distributed. The formula for the standard deviation (standard error) of the sampling distribution of the sample proportion is:

$\sigma_{\hat{p}} = \sqrt{\frac{p(1 - p)}{n}}$

where:

• $p$ is the population proportion,
• $n$ is the sample size.

However, the problem does not provide the population proportion ($p$), which is critical for calculating the standard error and solving this. Could you provide the population proportion ($p$)?

Once we have $p$, we can proceed with these steps:

2. Convert the proportions to z-scores

For each of the proportions (0.14 and 0.16), calculate the corresponding z-scores using:

$z = \frac{\hat{p} - p}{\sigma_{\hat{p}}}$

where $\hat{p}$ is the sample proportion, $p$ is the population proportion, and $\sigma_{\hat{p}}$ is the standard error.

3. Use the z-scores to find probabilities

After finding the z-scores for 0.14 and 0.16, we will use the standard normal distribution to find the area between those z-scores, which gives the probability.

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Please provide the population proportion ($p$) so I can continue with the calculation.