Respuesta :
Answer:
The minimum score for a student to receive A is 81.4.
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 = 75, \sigma = 5[/tex]
The department decides to give A to all students whose scores are in the top 10% on this exam.
What is the minimum score for a student to receive A?
The minimum score is the value of X when Z has a pvalue of 1-0.1 = 0.9. So it is X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 75}{5}[/tex]
[tex]X - 75 = 1.28*5[/tex]
[tex]X = 81.4[/tex]
The minimum score for a student to receive A is 81.4.
