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=_____.
There is no information which indicates mode.
The mean is 50. Two standard deviations is 12.
No on mode: in continous distributions, often the mode is defined as the mean. But in test scores, because it is not continous, most scores are not allowed (such as irrational numbers, decimal such as 65.3421 ), and scores are typically integers. I remember I Never gave a 50, it was always 49 or 51. So mode here, is ill defined without more information. I am not certain what a hypothetical normal distribution of test scores is....