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julia-pushkina [17]
3 years ago
13

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1504 and a standard devi

ation of 300. The local college includes a minimum score of 1954 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement
Mathematics
1 answer:
SVEN [57.7K]3 years ago
6 0

Answer:

6.68% of students from this school earn scores that satisfy the admission requirement

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

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:

\mu = 1504, \sigma = 300

The local college includes a minimum score of 1954 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement

This is 1 subtracted by the pvalue of Z when X = 1954. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{1954 - 1504}{300}

Z = 1.5

Z = 1.5 has a pvalue of 0.9332

1 - 0.9332 = 0.0668

6.68% of students from this school earn scores that satisfy the admission requirement

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What this means is that, we have a summation of the observed data and a summation of the frequency of data.

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