Using the Empirical Rule, it is found that the mean is of 64 inches and the standard deviation is of 3.2 inches.
What does the Empirical Rule state?
It states that, for a normally distributed random variable:
- Approximately 68% of the measures are within 1 standard deviation of the mean.
- Approximately 95% of the measures are within 2 standard deviations of the mean.
- Approximately 99.7% of the measures are within 3 standard deviations of the mean.
The normal distribution is symmetric, hence the mean is given by:
M = (57.6 + 70.4)/2 = 64.
57.6 is two standard deviations below the mean, hence the standard deviation is found as follows:
57.6 = 64 - 2s.
2s = 6.4
s = 3.2.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
#SPJ1
