A set of data has a normal distribution with a mean of 49 and a standard deviation of 8. Find the percent of data within the following interval.
From 25 to 73
The percent of data within the given interval is
3 answers
78.88%.
this is wrong
To find the percentage of data within the interval from 25 to 73 in a normal distribution with a mean of 49 and a standard deviation of 8, we need to find the z-scores for both values first.
Z-score for x = 25:
Z = (25 - 49) / 8
Z = -24 / 8
Z = -3
Z-score for x = 73:
Z = (73 - 49) / 8
Z = 24 / 8
Z = 3
Next, we look up the corresponding probabilities for z = -3 and z = 3 in a standard normal distribution table.
Probability for z = -3 is 0.0013
Probability for z = 3 is 0.9987
To find the percentage of data within the interval from 25 to 73, we calculate:
0.9987 - 0.0013 = 0.9974
Therefore, the percentage of data within the interval from 25 to 73 is 99.74%.
Z-score for x = 25:
Z = (25 - 49) / 8
Z = -24 / 8
Z = -3
Z-score for x = 73:
Z = (73 - 49) / 8
Z = 24 / 8
Z = 3
Next, we look up the corresponding probabilities for z = -3 and z = 3 in a standard normal distribution table.
Probability for z = -3 is 0.0013
Probability for z = 3 is 0.9987
To find the percentage of data within the interval from 25 to 73, we calculate:
0.9987 - 0.0013 = 0.9974
Therefore, the percentage of data within the interval from 25 to 73 is 99.74%.