Respuesta :
Answer:
D. $275
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 = 235, \sigma = 20[/tex]
According to the standard deviation rule, almost 2.5% of the students spent more than ... on textbooks in a semester:
This is the value of X when Z has a pvalue of 1-0.025 = 0.975. So it is X when Z = 1.96[/tex]
So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.96 = \frac{X - 235}{20}[/tex]
[tex]X - 235 = 20*1.96[/tex]
[tex]X = 274.2[/tex]
So the correct answer is:
D. $275
