Answer:
The scores that are less than or equal to 10.8 are considered significantly low.
The scores that are greater than or equal to 32.4 are considered significantly high.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 21.6
Standard Deviation, σ = 5.4
We are given that the distribution of score is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
Significantly low score:
[tex]z \leq -2\\z = \displaystyle\frac{x-21.6}{5.4} \leq -2\\\\\displaystyle\frac{x-21.6}{5.4} \leq -2\\\\x\leq -2(5.4) + 21.6\\\Rightarrow x \leq 10.8[/tex]
Thus, scores that are less than or equal to 10.8 are considered significantly low.
Significantly high score:
[tex]z \geq 2\\z = \displaystyle\frac{x-21.6}{5.4} \geq 2\\\\\displaystyle\frac{x-21.6}{5.4} \geq 2\\\\x\geq 2(5.4) + 21.6\\\Rightarrow x \geq 32.4[/tex]
Thus, scores that are greater than or equal to 32.4 are considered significantly high.
