Respuesta :
Answer:
5.8%
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:
[tex]\mu = 511, \sigma = 120[/tex]
Determine the probability that a randomly chosen high school student who took the SAT in 2015 will have a mathematics SAT score more than 700 points.
This is 1 subtracted by the pvalue of Z when X = 700.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{700 - 511}{120}[/tex]
[tex]Z = 1.575[/tex]
[tex]Z = 1.575[/tex] has a pvalue of 0.942
1 - 0.942 = 0.058
5.8% probability that a randomly chosen high school student who took the SAT in 2015 will have a mathematics SAT score more than 700 points.
