Suppose the scores of students on a Statistics course are Normally distributed with a mean of 563 and a standard deviation of 37
1 answer:
Answer:
47.72% of students scored between 563 and 637 on the exam .
Step-by-step explanation:
The percentage of the students scored between 563 and 637 on the exam
= The percentage of the students scored lower than 637 on the exam -
the percentage of the students scored lower than 563 on the exam.
Since 563 is the mean score of students on the Statistics course, 50% of students scored lower than 563. that is P(x<563)=0.5
P(x<637)=P(z<z*) where z* is the z-statistic of the score 637.
z score can be calculated using the formula
z*= where
- X =637
- M is the mean score (563)
- s is the standard deviation of the score distribution (37)
Then z*= =2
P(z<2)=0.9772, which means that 97.72% of students scored lower than 637 on the exam.
As a Result, 97.72%-50%=47.72% of students scored between 563 and 637 on the exam
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