Question

A Regional College uses the SAT to admit students to the school. The university notices that a lot of students apply even though they are not eligible. Given SAT scores are normally distributed, have a population mean of 500 and standard deviation of 100, what is the probability that a group of 12 randomly selected applicants would have a mean SAT score that is greater than 525 but below the current admission standard of 584?

Answer 1

0.191 is the probability that a group of 12 randomly selected applicants would have a mean SAT score that is greater than 525 but below the current admission standard of 584.

Explanation:

We are given the following information in the question:

Mean, μ = 500

Standard Deviation, σ = 100

n = 12

We are given that the distribution of SAT score is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(greater than 525 but 584)

Standard error due to sampling =

`\displaystyle(\sigma)/(√(n)) = (100)/(√(12))`

`P(525 < x < 584) = P(\displaystyle(525 - 500)/((100)/(√(12))) < z < \displaystyle(584-500)/((100)/(√(12)))) = P(0.866 < z < 2.909)\\\\= P(z \leq 2.909) - P(z < 0.866)\\= 0.998 - 0.807 = 0.191 = 19.1\%`

`P(525 < x < 584) = 19.1\%`

0.191 is the probability that a group of 12 randomly selected applicants would have a mean SAT score that is greater than 525 but below the current admission standard of 584.