Subject: Applied Mathematics 4

Topic: Probability

Difficulty: Medium

Let µ(meu) be the mean and σ standard deviation.
If x = 35(Marks), then z = (35-µ) / σ
If x = 60(Marks), then z = (60-µ) / σ

Since, we have a total of 100% so let's divide in into two parts as we have only parts in questions.
Now, we have 50% data on the left hand side and 50% of data on the right hand side. According to the question, we have 30% and 10% data as in the form of students. Now, we have (50% - 30%) = 20% of data on the left hand side and (50% - 10%) = 40% of data on the right hand side.


Area of the left hand side data graph is (35-µ) / σ = 0.50 - 0.30
that is, (35-µ) / σ = 0.20 = −1.2816 (Area of the graph)

Similarly, Area of the left hand side data graph is (60-µ) / σ = 0.50 - 0.10
that is, (60-µ) / σ = 0.40 = +1.0364 (Area of the graph)

Now, by combining both above equation, we get -
σ = 17.26 and µ = 62.11 which will be your required answer.