The combined SAT scores for the students at a local high school
are normally distributed with a mean of 1530 and a standard
deviation of 296. The local college includes a minimum score of 820
in its admission requirements.
What percentage of students from this school earn scores that
satisfy the admission requirement?
P(X > 820) = %
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.
Solution :
Given that,
mean = = 1530
standard deviation = = 296
P (x > 820 )
= 1 - P (x < 820 )
= 1 - P ( x - / ) < ( 820 - 1530 / 296)
= 1 - P ( z < -710 / 296 )
= 1 - P ( z < -2.399 )
Using z table
= 1 - 0.0082
= 0.9918
Probability = 0.9918 =99.18%
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