A normal distribution has a mean of 10 and a standard deviation of 1.5. Between which two values do 95% of the data fall ? And Between which two values do 68% of the data fall ?

Answer 1

In a normal distribution 68% of the values fall between -1 and +1 std deviation from the mean. If the std deviation is 1.5 and the mean is 10, then 68% will fall between 8.5 and 11.5.

Similarly, 95% fall between -2σ and +2σ, or ±3 from the mean. So the range for 95% would be between 7 and 13.