Question 1168124
standard deviation of the population is 8.
sample size is 84.
sample mean is 78.


the standard error is equal to the population standard deviation divided by the sample size.


this is equal to 8 / sqrt(84) = .8728715609


use a normal distribution calculator to find the proportion of scores between 76.702 and 79.298 when the mean score is 78 and the standard error of a sample size of 84 is equal to .8728715609.


your result will be that the proportion is equal to .8629972264.


that's your confidence level.


you are confident that 86.3% of samples of size 84 will have a mean that falls between 76.702 and 79.298.


100 - 86.3 = 13.7% of the samples will have a mean that falls outside these limits.


half of the 13.7% will fall below 76.782 and the other half of the 13.7% will fall above 79.298.


here's a display of the calculator results, rounded to whatever rounding rules the calculator has.


<img src = "http://theo.x10hosting.com/2020/102411.jpg" >



the online calculator says that the probability that the scores will be within those limits is .863.


round .8629972264. to 3 decimal digits and it becomes .863.


that online calculator can be found at <a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>


that calculator rounds the results to .863.


the TI-84 Plus calculator that i use (a physical calculator, not an online calculator, gave me the results rounded to a lot more decimal digits.


it does not, however, provided a nice online display such as the display from the online calculator.