select the correct answer.\nthe results of a series of surveys revealed a population with a mean of 4.73 and…

Explanation:

Step1: Calculate the standard error

The formula for the standard error of the mean is $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard - deviation and $n$ is the sample size. Given $\sigma = 0.865$ and $n = 200$, we have $\sigma_{\bar{x}}=\frac{0.865}{\sqrt{200}}\approx\frac{0.865}{14.142}\approx0.061$.

Step2: Determine the z - scores for 95% confidence interval

For a 95% confidence interval, the z - scores are $z=- 1.96$ and $z = 1.96$.

Step3: Calculate the lower and upper bounds of the confidence interval

The formula for the confidence interval of the sample mean is $\bar{x}\pm z\sigma_{\bar{x}}$. The lower bound is $\mu - z\sigma_{\bar{x}}=4.73-1.96\times0.061 = 4.73 - 0.11956\approx4.61$. The upper bound is $\mu + z\sigma_{\bar{x}}=4.73 + 1.96\times0.061=4.73+0.11956\approx4.85$.

Answer:

A. 4.88