Any even number raised to any power will remain even. (e.g. 2² = 4, 2³ = 8, etc)
Any odd number raised to any power will remain odd. (e.g. 1² = 1³ = ... = 1, 3⁴ = 81, etc)
So will always be even, since both
[even] - [odd] = [odd]
and
[odd] - [even] = [odd]
We have been given that the distribution of the number of daily requests is bell-shaped and has a mean of 38 and a standard deviation of 6. We are asked to find the approximate percentage of lightbulb replacement requests numbering between 38 and 56.
First of all, we will find z-score corresponding to 38 and 56.
Now we will find z-score corresponding to 56.
We know that according to Empirical rule approximately 68% data lies with-in standard deviation of mean, approximately 95% data lies within 2 standard deviation of mean and approximately 99.7% data lies within 3 standard deviation of mean that is .
We can see that data point 38 is at mean as it's z-score is 0 and z-score of 56 is 3. This means that 56 is 3 standard deviation above mean.
We know that mean is at center of normal distribution curve. So to find percentage of data points 3 SD above mean, we will divide 99.7% by 2.
Therefore, approximately of lightbulb replacement requests numbering between 38 and 56.