The physical plant at the main campus of a large state university receives daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 37 and a standard deviation of 3. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 37 and 40?
Do not enter the percent symbol.
Don't know what book says, but this is another way.
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z scores.
Multiply by 100.
Is this your book's rule?
Do you know the 68-95-99.7 rule? Approximately 68% of scores in normal distribution are within one standard deviation (34% on each side of the mean), 95% within 2 SD, and 99.7% within 3 SD.
To find the percentage of lightbulb replacement requests numbering between 37 and 40, we need to calculate the area under the bell-shaped curve between these two values.
According to the empirical rule (also known as the 68-95-99.7 rule), approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
In this case, the mean is 37, and the standard deviation is 3. So, the range between 37 and 40 is within one standard deviation of the mean.
Therefore, using the empirical rule, we can approximate that the percentage of lightbulb replacement requests numbering between 37 and 40 is approximately 68%.
To find the approximate percentage of lightbulb replacement requests numbering between 37 and 40, we can use the empirical rule, also known as the 68-95-99.7 rule.
According to the empirical rule, approximately:
- 68% of the data falls within one standard deviation of the mean,
- 95% falls within two standard deviations of the mean, and
- 99.7% falls within three standard deviations of the mean.
In this case, the mean is 37 and the standard deviation is 3.
To find the percentage of requests between 37 and 40, we need to calculate the proportion of requests falling within one standard deviation above and below the mean.
The range of one standard deviation above the mean is 37 + 3 = 40.
The range of one standard deviation below the mean is 37 - 3 = 34.
Therefore, the approximate percentage of lightbulb replacement requests numbering between 37 and 40 is approximately 68%.
Please note that this calculation assumes a normal distribution and the use of the empirical rule as presented in the book.