Answer :
Answer:
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.
Step-by-step 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:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
P(greater than 525 but 584)
Standard error due to sampling =
[tex]\displaystyle\frac{\sigma}{\sqrt{n}} = \frac{100}{\sqrt{12}}[/tex]
[tex]P(525 < x < 584) = P(\displaystyle\frac{525 - 500}{\frac{100}{\sqrt{12}}} < z < \displaystyle\frac{584-500}{\frac{100}{\sqrt{12}}}) = P(0.866 < z < 2.909)\\\\= P(z \leq 2.909) - P(z < 0.866)\\= 0.998 - 0.807 = 0.191 = 19.1\%[/tex]
[tex]P(525 < x < 584) = 19.1\%[/tex]
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.