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Oksi-84 [34.3K]
3 years ago
14

Suppose the scores of students on a Statistics course are Normally distributed with a mean of 563 and a standard deviation of 37

. What percentage of the students scored between 563 and 637 on the exam?
Mathematics
1 answer:
ololo11 [35]3 years ago
5 0

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*=\frac{X-M}{s} where

  • X =637
  • M is the mean score (563)
  • s is the standard deviation of the score distribution (37)

Then z*=\frac{637-563}{37} =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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