Question

The marks of students in a mathematical contest is taken to follow N( 60,100 ). A team has 3 students. Students are rewarded if their measure for the team is 75 and above. Find the probability that a team is rewarded

Answer 1

Let $X=$ the mark of student in a mathematical contest: $X\sim N(\mu,\sigma^2/n).$ Then

$Z=\dfrac{X-\mu}{\sigma/\sqrt{n}}\sim N(0,1)$

Given $\mu=60, \sigma^2=100, n=3$

$$P(X\geq75)=1-P(X<75)$$

$$=1-P(Z<\dfrac{75-70}{10/\sqrt{3}})$$

$$\approx1-P(Z<0.866)$$

$$\approx1-0.806762=0.193238$$

The probability that a team is rewarded is $0.193238.$