Mean and standard deviation, where the subjects are independent normal variates

[Muhanned]

I was trying to solve this question, but I was stuck when I red "INDEPENDENT NORMAL VARIATES". Can you please show me how to solve such question ?


The Mean and standard deviation of marks in English are 50 and 15 respectively. The corresponding values for Science module are 45 and 10 respectively. Assuming that the marks in the two subjects are independent normal variates. Find the probability that a student scores a total of marks lying between 100 and 120 in two subjects?

 

[Deleted member 4993]

I was trying to solve this question, but I was stuck when I red "INDEPENDENT NORMAL VARIATES". Can you please show me how to solve such question ?


The Mean and standard deviation of marks in English are 50 and 15 respectively. The corresponding values for Science module are 45 and 10 respectively. Assuming that the marks in the two subjects are independent normal variates. Find the probability that a student scores a total of marks lying between 100 and 120 in two subjects?

Please share your thoughts/work regarding this problem.

Independent variables would mean that the score of Science does not depend on score in english and vice-versa.

Normal variables would mean that

the score of Science is normally distributed and

score of english is normally distributed