In a certain population, 20% of the people are left-handed. (a) A random sample of size 50 is drawn from this population. Let X represent the number of left-handed people in the sample. Use the...

In a certain population, 20% of the people are left-handed.

(a) A random sample of size 50 is drawn from this population. Let
X
represent

the number of left-handed people in the sample. Use the central limit theorem

to approximate:

i. Pr[12
X
20]

ii. Pr[12
X
20]

(b) Use Table A.2 in the Appendix to find the exact probabilities.

(c) Considering your answers to (a) and (b), mention a possible shortcoming of

the central limit theorem when it is applied to a discrete random variable.