Respuesta :
Answer:
The minimum score required for the scholarship is 29.306.
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 = 21.4, \sigma = 5.9[/tex]
What is the minimum score required for the scholarship
This is X when Z has a pvalue of 1-0.09 = 0.91. So it is X when Z = 1.34.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.34 = \frac{X - 21.4}{5.9}[/tex]
[tex]X - 21.4 = 1.34*5.9[/tex]
[tex]X = 29.306[/tex]
The minimum score required for the scholarship is 29.306.
