Respuesta :
Answer:
The cutoff score for recruitment by the statistics department is 675.
Step-by-step explanation:
Problems of normally distributed samples can be 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 = 500, \sigma = 100[/tex]
Cutoff score for the top 4%.
100-4 = 96th percentile, which is X when Z has a pvalue of 0.96. So X when Z = 1.75.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.75 = \frac{X - 500}{100}[/tex]
[tex]X - 500 = 1.75*100[/tex]
[tex]X = 675[/tex]
The cutoff score for recruitment by the statistics department is 675.
