Respuesta :
Answer:
The minimum score needed to be considered for admission to Stanfords graduate school is 328.48.
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]\mu = 303, \sigma = 13[/tex]
What is the minimum score needed to be considered for admission to Stanfords graduate school?
Top 2.5%.
So X when Z has a pvalue of 1-0.025 = 0.975. So X when Z = 1.96
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 303}{13}[/tex]
[tex]X - 303 = 13*1.96[/tex]
[tex]X = 328.48[/tex]
The minimum score needed to be considered for admission to Stanfords graduate school is 328.48.
