Respuesta :
Answer:
history test
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:
He did better relative to the class in the test in which he had a higher Z score.
So:
History
Raul received a score of 75 on a history test for which the class mean was 70 with a standard deviation of 7. So we have [tex]X = 75, \mu = 70, \sigma = 7[/tex]
So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{75 - 70}{7}[/tex]
[tex]Z = 0.71[/tex]
Biology
He received a score of 73 on a biology test for which the class mean was 70 with standard deviation 7. So we have [tex]X = 73, \mu = 70, \sigma = 7[/tex]
So:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{73 - 70}{7}[/tex]
[tex]Z = 0.43[/tex]
He had a higher Z score in the history test, so this is the test in which he did better relative to the rest of the class.
