A set of data has a normal distribution with a mean of 46 and a standard deviation of 9. Find the percent of data within the following interval.

from 37 to 55

1 answer

To find the percent of data within the interval from 37 to 55 in a normal distribution with a mean of 46 and a standard deviation of 9, we first need to find the z-scores corresponding to the two values.

For 37:
z = (37 - 46) / 9 = -1

For 55:
z = (55 - 46) / 9 = 1

Next, we find the area under the normal curve between these two z-scores. We can do this by finding the area to the left of z = 1 (which is 0.8413) and subtracting the area to the left of z = -1 (which is 0.1587).

Therefore, the area between z = -1 and z = 1 is 0.8413 - 0.1587 = 0.6826.

To find the percent of data within the interval from 37 to 55, we multiply this by 100:
0.6826 * 100 = 68.26%

So, approximately 68.26% of the data falls within the interval from 37 to 55 in a normal distribution with a mean of 46 and a standard deviation of 9.