A population proportion is .04 A sample size of 150 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 +-0.03 of the population proportion?
b. What is the probability that the sample proportion will be within +-0.06 of the population proportion?
ANSWER:
Given that,
population proportion , =0.4
random sample size=n=150
a probability that the sample proportion will be within +-0.03 of the population proportion:
sample proportion Ps will lie within 0.4-0.03=0.37 and 0.4+0.03=0.43
p=0.4 , q=0.6
,S.D= =(0.4*0.6)/150 =0.04
P(0.37<Ps<0.43)=P( 0.37-0.4/ 0.04< Z<0.43-0.4 /0.04 ) =P(-0.75<Z<0.75)
=P(Z<0.75) - P(Z<-0.75) = 0.7734-0. 2266=0.5468
probability that the sample proportion will be within +-0.03 of the population proportion is 54.68%
b. probability that the sample proportion will be within +-0.06 of the population proportion:
sample proportion Ps will lie within 0.4-0.06=0.34 and 0.4+0.06=0.46
P(0.34<Ps<0.46)=P( 0.34-0.4/ 0.04< Z<0.46-0.4 /0.04 ) =P(-1.5<Z<1.5)
=P(Z<1.5) - P(Z<-1.5) = 0.9932-0.0668=0.9264
probability that the sample proportion will be within +-0.06 of the population proportion is 92.64%
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