Question

19. Generation Y has been defined as those individuals who were born between 1981 and 1991. A 2010 survey by a credit counseling foundation found that 58% of the young adults in Generation Y pay their monthly bills on time) Suppose we take a random sample of 220 people from Generation Y. Complete parts a through e below.

a. Calculate the standard error of the proportion. σp = (Round to four decimal places as needed.)

b. What is the probability that 135 or fewer will pay their monthly bills on time?

P(135 or fewer Generation Y individuals will pay their monthly bills on time) = (Round to four decimal places as needed.)

c. What is the probability that 110 or fewer will pay their monthly bills on time?

P(110 or fewer Generation Y individuals will pay their monthly bills on time) = (Round to four decimal places as needed.)

d. What is the probability that 132 or more will pay their monthly bills on time?

P(132 or more Generation Y individuals will pay their monthly bills on time) = (Round to four decimal places as needed.)

e. What is the probability that between 125 and 134 of them will pay their monthly bills on time?

P(Between 125 and 134 of them will pay their monthly bills on time) = (Round to four decimal places as needed.)

Answer 1

a)

std error of proportion=σp=√(p*(1-p)/n)=

0.0333

b)

n=

220

p=

0.5800

here mean of distribution=μ=np=	127.60
and standard deviation σ=sqrt(np(1-p))=	7.32
for normal distribution z score =(X-μ)/σx

therefore from normal approximation of binomial distribution and continuity correction:

probability =P(X<135.5)=(Z<(135.5-127.6)/7.321)=P(Z<1.08)=0.8599

c)

probability =P(X<110.5)=(Z<(110.5-127.6)/7.321)=P(Z<-2.34)=0.0096

d)

probability =P(X>131.5)=P(Z>(131.5-127.6)/7.321)=P(Z>0.53)=1-P(Z<0.53)=1-0.7019=0.2981

e)

probability =P(124.5<X<134.5)=P((124.5-127.6)/7.321)<Z<(134.5-127.6)/7.321)=P(-0.42<Z<0.94)=0.8264-0.3372=0.4892