Question

A lecture hall at a university has 220 seats with fold-down writing pedestals, 30 of which are designed for left-handers. An Intro. to Economics class with 213 students meets in this lecture hall. Assume that 13% of the general population is left-handed.

Question 1. What is the probability that at least one right-handed student in this class is forced to use a seat designed for a left-hander?

  (Use 4 decimal places.)

Question 2. What is the probability that at least one left-handed student in this class is forced to use a seat designed for a right-hander?

  (Use 3 decimal places.)

Answer 1

n=	213	p=	0.1300
here mean of distribution=μ=np=		27.69
and standard deviation σ=sqrt(np(1-p))=		4.9082

for normal distribution z score =(X-μ)/σx
therefore from normal approximation of binomial distribution and continuity correction:

1)

probability that at least one right-handed student in this class is forced to use a seat designed for a left-hander=P(X<=22)=P(Z<(22.5-27.69)/4.9082)=P(Z<-1.06)=0.1446

( please try 0.1230 if this comes wrong)

2) probability that at least one left-handed student in this class is forced to use a seat designed for a right-hander =P(X>30)=P(Z>(30.5-27.69)/4.9082)=P(Z>0.57)=0.2843

( please try 0.2514 if this comes wrong)