Fifty percent of households say they would feel secure if they had $50,000 in savings. you randomly select 8 households and ask them if they would feel secure if they had $50,000 in savings. find the probability that the number that say they would feel secure is (a) exactly five, (b) more than five, and (c) at most five
Accepted Solution
A:
Step-by-step Answer:"Fifty percent of households say they would feel secure if they had $50,000 in savings." => population mean for satisfaction is 0.50.N = number of household asked.x = number of satisfied households.Use binomial probability, B(x,N,p) = C(N,x)*(p^x)*(1-p)^(N-x)For 8 households and 3 questions (a), (b), and (c), we can tabulate all values of x and extract answers from there.x B(x,8,0.5) cumulative probability0 0.00390625 0.003906251 0.03125 0.035156252 0.109375 0.144531253 0.21875 0.363281254 0.2734375 0.636718755 0.21875 0.855468756 0.109375 0.964843757 0.03125 0.996093758 0.00390625 1.0From the table, we see clearly that(a) probability P(x=5)=0.2188(b) probability P(x>5)=1-0.8555=0.1445(c) probability P(x<=5) = 0.8555Note: All answers above have been rounded to the nearest 4 places of decimals.