- A large number of students sat an examination. All of the students answered the first question. The first question was answered correctly by \(40 \%\) of the students.
In a random sample of 20 students who sat the examination, \(X\) denotes the number of students who answered the first question correctly.
- Write down the distribution of the random variable \(X\)
- Find \(\mathrm { P } ( 4 \leqslant X < 9 )\)
Students gain 7 points if they answer the first question correctly and they lose 3 points if they do not answer it correctly.
- Find the probability that the total number of points scored on the first question by the 20 students is more than 0
- Calculate the variance of the total number of points scored on the first question by a random sample of 20 students.