Answer:
The minimum score that she must earn to get admitted is 523.
Step-by-step explanation:
As the scores are normally distributed, we can calculate the probability using the z-score.
The distribution has a mean of 420 and a standard deviation of 80.
We have to calculate the z-score z* that satisfies:
[tex]P(z>z^*)=0.1[/tex]
This happens for z*=1.28155.
Then, we can calculate the score as:
[tex]X=\mu+z\cdot\sigma=420+1.28155\cdot 80=420+102.524=522.524[/tex]
