Respuesta :
Using the Empirical Rule and the Central Limit Theorem, we have that:
- About 68% of the sample mean fall with in the intervals $1.64 and $1.82.
- About 99.7% of the sample mean fall with in the intervals $1.46 and $2.
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.
What does the Central Limit Theorem state?
By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, the standard deviation of the distribution of sample means is:
[tex]s = \frac{0.657}{\sqrt{50}} = 0.09[/tex]
68% of the means are within 1 standard deviation of the mean, hence the bounds are:
- 1.73 - 0.09 = $1.64.
- 1.73 + 0.09 = $1.82.
99.7% of the means are within 3 standard deviations of the mean, hence the bounds are:
- 1.73 - 3 x 0.09 = $1.46.
- 1.73 + 3 x 0.09 = $2.
More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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