Respuesta :
Answer:
A. 0.317.
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 tha:
[tex]\mu = 515, \sigma = 109[/tex]
The proportion of students scoring between 460 and 550 is closest to
This is the pvalue of Z when X = 550 subtracted by the pvalue of Z when X = 460. So
X = 550
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{550 - 515}{109}[/tex]
[tex]Z = 0.32[/tex]
[tex]Z = 0.32[/tex] has a pvalue of 0.6255
X = 460
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{460 - 515}{109}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a pvalue of 0.3085
0.6255 - 0.3085 = 0.317
