Question

Forty-six percent of a population possesses a particular characteristic. Random samples are taken from this population. Determine the probability of each of the following occurrences. Appendix A Statistical Tables (Round all z values to 2 decimal places. Round all intermediate calculations and answers to 4 decimal places.) a. The sample size is 60 and the sample proportion is between .41 and .53. p = b. The sample size is 458 and the sample proportion is less than .40. p = c. The sample size is 1350 and the sample proportion is greater than .49. p =

Answer 1

p = 0.46

? = sqrt(p*(1-p)/n)

a) p1 = 0.41 and p2=0.53

n=60

? = sqrt(p*(1-p)/n)= sqrt(0.46*0.54/60) = 0.064

Z1 = (p1-p)/? = (0.41-0.46)/0.064= -0.781

Z2 = (p2-p)/? = (0.53-0.46)/0.064= 1.093

P(-0.781<Z<1.093) = P(Z<1.093) - P(Z<-0.781) = 0.8621 - 0.2177 = 0.6444

b) n=458

? = sqrt(p*(1-p)/n)= sqrt(0.46*0.54/458) = 0.023

Z = (p1-p)/? = (0.4-0.46)/0.023= -2.6

P(Z<-2.6) = 0.0047

c)

n=1350

? = sqrt(p*(1-p)/n)= sqrt(0.46*0.54/1350) = 0.0135

Z = (p1-p)/? = (0.49-0.46)/0.0135= 2.22

P(Z>2.22) = 1-P(Z<2.22) = 1- 0.9868= 0.0132

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