Question On standard pf error & Sample means/population means!?

A: Standard error of the sample is given approximately as  ..... 

Standard deviation sample divided by the square root of number of samples 

https://errorcodespro.com/how-to-calculate-standar...

Standard error = SD/√(n) = 1.77/√(555) = 0.0751 

B: Confidence interval for sample population mean 

The mean of a sample may not coincide exactly with the mean of a huge population. A percentage confidence interval is a range of values that you can be certain to that percentage that the sample mean contains the true mean of the population. When we calculate a 95% confidence interval for the population mean it is not the same as a range of the full population that contains 95% of the values. The standard error from A can be regarded as the new standard deviation of the sampling distribution.(Helpful simple example within this link)  

http://onlinestatbook.com/2/estimation/mean.html 

To calculate the confidence interval we use the fact that 95% of the area of the sample distribution, (assumed normal), is within 1.96 of the new standard deviations either side of the mean. So the calculations of the interval are 

2.89 – 1.96*0.0751 = 2.4427 

2.89 + 1.96*0.0751 = 2.7373 which you could write as 

2.89 ± 0.1472 

Males sampled think that ideal number of children is between 2.44 and 2.74