Question

A population proportion is 0.4 A sample of size 250 will be taken and the sample proportion  will be used to estimate the population proportion. Use z-table.

Round your answers to four decimal places. Do not round intermediate calculations.

a. What is the probability that the sample proportion will be within +- .04 of the population proportion?

b. What is the probability that the sample proportion will be within +- .06 of the population proportion?

Answer 1

here population proportion=     μp=	0.4000
sample size       =n=	250
std error of proportion=σp=√(p*(1-p)/n)=	0.0310

a)

probability =P(0.36<X<0.44)=P((0.36-0.4)/0.031)<Z<(0.44-0.4)/0.031)=P(-1.29<Z<1.29)=0.9015-0.0985=0.8030

b)

probability =P(0.34<X<0.46)=P((0.34-0.4)/0.031)<Z<(0.46-0.4)/0.031)=P(-1.94<Z<1.94)=0.9738-0.0262=0.9476