Answer:
C. 1350
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.
In this problem, we have that:
[tex]X = 2230[/tex]
Your best option?
You want the higher z-score for yourself, which means that your grade is in a higher percentile and you are more likely to be accepted.
Assuming they all have the same standard deviations, your best option is in the college with the lowest average score, which is [tex]\mu[/tex]
So the correct answer is:
C. 1350
