Question

10. Working two jobs: About 12% of employed adults in the United States held multiple jobs. A random sample of 65 employed adults is chosen. 1) Is it appropriate to use the normal approximation to find the probability that less than 5% of the individuals in the sample hold multiple jobs? If so, find the probability. If not, explain why not. II) A new sample of 200 employed adults is chosen. Find the probability that less than 5% of the individuals in this sample hold multiple jobs. III) Find the probability that more than 4.5% of the individuals in the sample of 200 hold multiple jobs. iv) Find the probability that the proportion of individuals in the sample of 200 who hold multiple jobs is between 14% and 17%. v) Would it be unusual if less than 10% of the individuals in the sample of 200 held multiple jobs?

Answer 1

-(i) Sample size n=65 Success probly p=0.12 - np = 7.8 ; n(ip) = 65x (10.12) = 57.2 = np25 & nlip) 25; 2 Yes, it is apo mo nute to use Normal approx... Pr L P<0.05] = P [ Pol < = p [2<-1.736] Polê caos] = 0.041 La) n = 200, 2 x N 0 0 1 acc 50 = 0,2231) Pr [p <0.us] = P [2 < 2 ose 3 = P [Z<-3,047] = 0.001 _in) P. [å 70.045] = Pr [ 2 30045-02] =P [ 27-3.265) = 0.999 EN) P (0.14 s § 50.17] = P [ 14 27 C Z ? 0.19 0 1 = P 0.87 LZL 2.176] - 0.177 (v) Po l Å< 0,10] = P. [ Z < -0.02 - P(Z <6087)] (f [ p< 0.10] = 0.1927 Unsual. Since Probty is not too small; It Won't Be -0.02297 of less than loy held multiple jobs