Can you please check if my work is right?

A large lecture theater has230seats,21of which can accomodate left-handed students. Suppose it is known that12% of people are left-handed. One class held in the theater has209students. (a) LetXbe the number of left-handed students in the class. What are the mean and standard deviation ofX? (b) Letbe theproportion of left-handed students in the class. What are the mean and standard deviation of? (c) What is the approximate probability that all left-handed students in the class get an appropriate desk?

Answer

a)

Mean is 209 x 0.12 = 25.08

Standard Deviation is square root of 25.08 multiples by (1-0.12)

Standard Deviation if4.6979

b)

The mean of p hat is 0.12

Standard Deviation is square rood of 0.12 x (1-0.12) divided by 209

Standard deviation of p hat is 0.0225

c)

21 - 25.08 divided by4.6979

- 0.87 look at table A to find z score and probability

probability is 0.1922