The scores on a standardized test are normally distributed. If a random sample of standardized test scores is taken and the confidence interval is (497,537), what is the sample mean x¯?

The sample mean

Step-by-step explanation:

The confidence interval is given by :-

Sample mean ± Margin of error

Given : The scores on a standardized test are normally distributed. If a random sample of standardized test scores is taken and the confidence interval is (497,537).

i.e. Sample mean - Margin of error = 497  ..(i)

Sample mean + Margin of error=537  ..(ii)

Adding (1)  and (2), we get

2 (Sample mean) = 1034

⇒Sample mean = 517

Hence, the sample mean

3 is greater then both of those numbers