Homework SourseThe average score of 100 students taking a statistics final
The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. assuming a normal distribution , what test score separates the top 25% of the students from the lower 75% of students?
The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. assuming a normal distribution , what test score separates the top 25% of the students from the lower 75% of students?
Solution
In a normal distribution, the probability of a statistic, the Z random variable, is equal to: Z = (X - µ)/s where µ = mean, and s = standard distribution. you are asking for 25% = (X - µ)/s 25% = 0.6745 (from the normal distribution table) (X - µ)/s = 0.6745 (X - 70) / 7 = 0.6745 (X - 70) = 0.6745*7 = 4.7215 (X) = 4.7215+70 = 74.7215 the top 25% achieve a score of 75 or higher (rounded up).
