Respuesta :
Answer:
The observation would be considered unusual because it is farther than three standard deviations from the mean.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When Z has an absolute value higher than 2, the observation is considered unusual.
In this problem, we have that:
[tex]\mu = 5, \sigma = 2, X = 12[/tex]
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{12 - 5}{2}[/tex]
[tex]Z = 3.5[/tex]
So the correct answer is:
The observation would be considered unusual because it is farther than three standard deviations from the mean.
The correct statement is,
The observation would be considered unusual because it is farther than three standard deviations from the mean.
Normal distribution:
The given question is based on normally distributed samples .
the normally distributed samples are solved by using the z-score formula.
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where [tex]\mu[/tex] is mean, and [tex]\sigma[/tex] is standard deviation.
Given that, [tex]X=12,\mu=5,\sigma=2[/tex]
Substitute values in z-score formula.
[tex]z=\frac{12-5}{2} \\\\z=\frac{7}{2} \\\\z=3.5[/tex]
Since, z-score measures how many standard deviations the measure is from the mean.
Therefore, the observation would be considered unusual because it is farther than three standard deviations from the mean.
Learn more about the z-score here:
https://brainly.com/question/25638875
