what is the percentage of scores between two numbers if you have a mean and standard deviation

Question

the question is "If the mean is 90 and the standard deviation is 5, what percent of the scores are between 75 and 105?

I know the answer is 99.7% but my question is HOW do i find that answer?

Answer 1

75 is 90 - 15 = 90 - 3x5 so 3 standard deviations below the mean

105 = 90 + 15 = 90 + 3 x 5 = 3 standard deviations above the mean

In a standard normal, 99.7% of data is within 3 standard deviations of the mean [ standard result ]