High School

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The combined SAT scores for the students at a local high school are normally distributed with a mean of 1495 and a standard deviation of 305. The local college includes a minimum score of 794 in its admission requirements.

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

P(X < 794) = _________ %

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer :

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1495 and a standard deviation of 305. The local college includes a minimum score of 794 in its admission requirements.

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

P(X < 794) = 1.1 %

To answer this question, we need to calculate the z-score, which is a measurement of how many standard deviations an observation is away from the mean. The formula for calculating the z-score is:

Z = (X - μ) / σ

where X is the observation, μ is the mean, and σ is the standard deviation.

Plugging the given values into this formula gives us:

Z = (794 - 1495) / 305 = -2.3

This means that a score of 794 is 2.3 standard deviations below the mean. To find the percentage of students who earn scores below this, we refer to a standard normal distribution table, which shows us that a z-score of -2.3 corresponds to approximately 1.1%.

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