Question
with a mean of 67 and a standard deviation of 11 use the 68-95-99.7 rule to find out what percentage is greater than 78
Answers
GPT 3.5
To apply the 68-95-99.7 rule, we need to assume that the data follows a normal distribution. The rule states that within one standard deviation (68% of the data), 34% is on each side of the mean. Within two standard deviations (95% of the data), 2.5% is on each side of the mean. Within three standard deviations (99.7% of the data), 0.15% is on each side of the mean.
Given a mean of 67 and a standard deviation of 11, we want to find the percentage greater than 78. To do this, we need to find the area to the right of 78 on the normal distribution curve.
First, we need to calculate the z-score for 78:
z = (X - μ) / σ
z = (78 - 67) / 11
z = 1
The z-score of 1 indicates that 78 is one standard deviation above the mean. From the 68-95-99.7 rule, we know that within one standard deviation, 34% of the data lies on each side of the mean. Therefore, 34% of the data is to the right of 67.
Since 78 is exactly one standard deviation above the mean, only a portion of that 34% is greater than 78. Since the normal distribution is symmetrical, we can assume that this portion is half of 34%, which is 17%.
Thus, the percentage of data greater than 78 is approximately 17%.
Given a mean of 67 and a standard deviation of 11, we want to find the percentage greater than 78. To do this, we need to find the area to the right of 78 on the normal distribution curve.
First, we need to calculate the z-score for 78:
z = (X - μ) / σ
z = (78 - 67) / 11
z = 1
The z-score of 1 indicates that 78 is one standard deviation above the mean. From the 68-95-99.7 rule, we know that within one standard deviation, 34% of the data lies on each side of the mean. Therefore, 34% of the data is to the right of 67.
Since 78 is exactly one standard deviation above the mean, only a portion of that 34% is greater than 78. Since the normal distribution is symmetrical, we can assume that this portion is half of 34%, which is 17%.
Thus, the percentage of data greater than 78 is approximately 17%.