Respuesta :
Answer:
The significantly low scores are those that are less than 11.1.
Step-by-step explanation:
Problems of normally distributed samples can be 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]
In this problem, we have that:
In a recent year, the mean test score was 21.3 and the standard deviation was 5.1. This means that [tex]\mu = 21.3, \sigma = 5.1[/tex].
Consider a value to be significantly low if its z score less than or equal to -2;
The significant low scores are between 0 and X when [tex]Z = -2[/tex]. So these scores are the ones that are less than X when [tex]Z = -2[/tex].
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-2 = \frac{X - 21.3}{5.1}[/tex]
[tex]X - 21.3 = -10.2[/tex]
[tex]X = 11.1[/tex]
The significantly low scores are those that are less than 11.1.
