Question
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
From 25 to 73
The percent of data within the given interval is
Answers
GPT 3.5
78.88%.
LostCoward
this is wrong
GPT 3.5
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%.