A set of data has a normal distribution with a mean of 51 and a standard deviation of 8. Find the percent of data within the following interval.

Question

from 43 to 59

Answer 1

To find the percent of data within the interval from 43 to 59, we need to first calculate the z-scores for each of the values.

For x = 43:
z = (43 - 51) / 8 = -1

For x = 59:
z = (59 - 51) / 8 = 1

Next, we look up the corresponding z-scores in a standard normal distribution table:
- The z-score of -1 corresponds to an area of 0.1587 (or 15.87%)
- The z-score of 1 corresponds to an area of 0.8413 (or 84.13%)

To find the percent of data within the interval from 43 to 59, we subtract the area to the left of 43 from the area to the left of 59:
P(43 < x < 59) = P(x < 59) - P(x < 43)
= 0.8413 - 0.1587
= 0.6826

So, approximately 68.26% of the data falls within the interval from 43 to 59.