Respuesta :
Answer:
The minimum score required for admission is 558.75.
Step-by-step explanation:
When the distribution is normal, we use 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.
Suppose SAT Critical Reading scores are normally distributed with a mean of 501 and a standard deviation of 110.
This means that [tex]\mu = 501, \sigma = 110[/tex]
A university plans to admit students whose scores are in the top 30%. What is the minimum score required for admission
This is the 100 - 30 = 70th percentile, which is X when Z has a pvalue of 0.7. So X when Z = 0.525. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.525 = \frac{X - 501}{110}[/tex]
[tex]X - 501 = 0.525*110[/tex]
[tex]X = 558.75[/tex]
The minimum score required for admission is 558.75.
