Respuesta :
Answer:
The interval that contains the middle 68% of the heights is from 50 inches to 64 inches
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 57
Standard deviation = 7
Use the Empirical Rule to determine the interval that contains the middle 68% of the heights
Within 1 standard deviation of the mean
57 - 7 = 50 inches
57 + 7 = 64 inches
The interval that contains the middle 68% of the heights is from 50 inches to 64 inches
Answer:
Step-by-step explanation:
The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below
68% of data falls within the first standard deviation from the mean.
95% fall within two standard deviations.
99.7% fall within three standard deviations.
From the information given, the mean is 57 inches and the standard deviation is 7 inches.
the interval that contains the middle 68% of the heights would fall within one standard deviation.
1 standard deviation = 7
57 - 7 = 50
57 + 7 = 64
Therefore, the interval that contains the middle 68% of the heights would fall within 50 and 64 inches
