Question 1200611
mean is 488 and standard deviation is 67.
99.7% of the exam scores lie between 289.162 and 686.838
critical z-score for two tailed confidence interval os .997 is equal to plus or minus 1.967737927.
low z-score formula becomes -2.967737927 = (x - 488) / 67.
solve for x to get x = 67 * -2.967737927 + 488 = 289.163
high z-score formula becomes 2.967737927 = (x - 488) / 67.
solve for x to get x = 67 * 2.967737927 + 488 = 686.838.
i did it the easy way by using the calculator at <a href = "https://davidmlane.com/hyperstat/z_table.html" target = "_blank">https://davidmlane.com/hyperstat/z_table.html</a>
here are the results from using that calculator.
<img src = "http://theo.x10hosting.com/2023/022702.jpg">