SOLUTION: Suppose the scores of students on an exam are Normally distributed with a mean of 488 and a standard deviation of 67. Then approximately 99.7% of the exam scores lie between the nu

Question 1200611: Suppose the scores of students on an exam are Normally distributed with a mean of 488 and a standard deviation of 67. Then approximately 99.7% of the exam scores lie between the numbers
and
such that the mean is halfway between these two integers.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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 https://davidmlane.com/hyperstat/z_table.html
here are the results from using that calculator.

RELATED QUESTIONS
The scores on an exam are normally distributed, with a mean of 77 and a standard... (answered by Edwin McCravy)

Suppose the scores of students on an exam are Normally distributed with a mean of 436 and (answered by Theo)

A professor finds that the scores on a History exam are known to be normally distributed... (answered by stanbon)

The scores on an exam are normally distributed, with a mean of 79 and a standard... (answered by rapaljer)

The scores on an exam are normally distributed, with a mean of 77 and a standard... (answered by scott8148)

A class of 200 students takes an exam. The students' scores are normally distributed with (answered by stanbon)

Suppose the scores of students on a Statistics course are Normally distributed with a... (answered by Glaviolette)

Hi. Please help me solve stats question Suppose scores on exams in statistics are... (answered by Theo)

The scores of students on an exam are normally distributed with a mean of 384 and a... (answered by Boreal)