A large lecture theater has 230 seats, 23 of which can accomodate left-handed students. Suppose it is known that 13% of people are left-handed. One class held in the theater has 209 students.

(a) Let X be the number of left-handed students in the class. The mean and standard deviation of X are, respectively,

Question

A large lecture theater has 230 seats, 23 of which can accomodate left-handed students.  Suppose it is known that 13% of people are left-handed.  One class held in the theater has 209 students.

(a) Let X be the number of left-handed students in the class.  The mean and standard deviation of X are, respectively,

kropot72 · Answer

The probability of a student being left-handed is 0.13. The binomial distribution applies to this question. The binomial distribution can be approximated by the normal distribution in this case where
$$mean=np=209\times0.13$$
and
$$standard\ deviation=\sqrt{np(1-p)}=\sqrt{209\times0.13\times0.87}$$

kropot72 · Answer

Note: It seems that any overflow of the seats for left-handed students would need to be accommodated in the seats for the right-handed.

anonymous · Answer

@kropot72 and that is likely to happen with a high probability (77% using exact binomial for P(x>=24))
All that besides all the guys that never take notes in class and do not really care whether the chair is for left or right-handed :)

kropot72 · Answer

@CarlosGP Agreed :0

bambimonster · Answer

i got it already thanks a bunch

kropot72 · Answer

You're welcome :)