  A test has been devised to measure a student's level of motivation during high school. The motivation scores on this test are approximatley normally distributed with a mean of 40 and a standard deviaton of 10. The higher the score the greater the motivation to do well in school. What percentage of students taking his test will score between 35 and 50?

Question

A test has been devised to measure a student's level of motivation during high school. The motivation scores on this test are approximatley normally distributed with a mean of 40 and a standard deviaton of 10. The higher the score the greater the motivation to do well in school. What percentage of students taking his test will score between 35 and 50?

Step 1

Denote X as the motivation scores on this test. It is given that X is normally distributed, with mean μ = 40 and standard deviation σ = 10.

Step 2

The probability that the score will be between 35 and 50 is,

Step 3

Therefore, 53.73% of the students w...

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