For a hypothetical normal distribution of test scores, approximately 95% fall between 38 and 62, 2.5% are below 38, and 2.5% are above 62. Given this information, (a) the mode=_____ and (b) the standard deviation=_____.

Answer 1

Mean = (38 + 62)/2 = 100/2 = 50

50 - 38 = 12 = 2 standard deviations below the mean.

62 - 50 = 12 = 2 standard deviations above the mean.

Therefore, 1 standard deviation = 6

I hope this helps.

Answer 2

Yes, I understand how you worked out the mean. I understand about the 12
above and below the mean, but how did you arrive at 12 = 2 standard deviation points.