The combined SAT scores for the students at a local high school are normally distributed with a mean of 1488 and a standard deviation of 309. The local college includes a minimum score of 1457 in its admission requirements.

What percentage of students from this school earn scores that satisfy the admission requirement?

\[ P(X > 1457) = \]

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.

Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.

The mean and the standard deviation for this problem are given as follows:

[tex]\mu = 1488, \sigma = 309[/tex]

The proportion of scores above 1457 is one subtracted by the p-value of Z when X = 1457, hence:

Z = (1457 - 1488)/309

Z = -0.1

Z = -0.1 has a p-value of 0.4602.

Hence:

1 - 0.4602 = 0.5398 = 53.98%.

More can be learned about the normal distribution at https://brainly.com/question/25800303

#SPJ1