Question

It is given that the total marks of all probability students have an average of 45 marks with a standard deviation of 15 marks. If a student from a sample of 9 students is chosen at random, what is the probability that his marks are between 40 and 60?

Answer 1

$P(40<X<60)=P(\frac{40-45}{\frac{15}{\sqrt{9}}}<Z<\frac{60-45}{\frac{15}{\sqrt{9}}})=P(-1<Z<3)=$

$=P(Z<3)-P(Z<-1)=0.8400.$