Question
etat to chaftey Fall 2017 Homework: Homework #11 Score: 0.5 of 1 pt 80t 8 (8 complete) HW Score: 72 5%, 58 8.2.16-T Accoding to a study conducted by a stafistical organization, the proportion of people who are satisied with the way things are going in their ives is 0.88 Suppo random sample of 100 people is obtained Complete parts (a) through (e) below leel dilerenly segarding their satistaction DThe sample proportion p is a random varisble because the value of p represents a random person incloded in the sample. The varability s due to the fa hat people may not be responding to the question truthfully (c) DesciRe the sampling distribution of p, the proportion of people who are satisied with the way things are going in their lfe Be sure to veriy the model reqarements S ce the sample size is no more than 5% of the popula on size and p 1-p): 12.04 2 10, the dstribution of p is appro imately no nal with p =860 ar e 0035 Round to three decimal places as needed.) d n the sample obtained in part a what is the probability that the proportion who are satisfied with the way things are going n their life ceeds 0 to? The probability that the proportion who are satishied with the way things sre going in their life exceeds 0 88 is 0.2822 Round to four decimal plsces as needed) uing the doit tion tom parl Ic would it be unusual ror a survey cd 100 people to reveal that 80 or fewer people is the sample are sasted with their hes? TI-pobabiny that 80 or tewer poogle in the sample are satisfied is unusual because this probablity- ess than ' % t which to four decimal places as needed) ne in the answer box and then clck Check Arswer as showing
Explanation / Answer
(c) here p=0.86 and n=100
so standard deviation=sd(p)=sqrt(p(-p)/n)=sqrt(0.86*(1-0.86)/100)=0.0347
(d) P(p>0.88)=P(Z>0.5764)=1-P(Z<0.5764)=1-0.7178=0.2822
z=(0.88-0.86)/0.0347=0.5764
(e) for p=0.8, z=(0.8-0.86)/0.0347=-1.7291
P(p<0.8)=P(Z<-1.7291)=0.0419
