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 probability
0 0.00390625 0.00390625
1 0.03125 0.03515625
2 0.109375 0.14453125
3 0.21875 0.36328125
4 0.2734375 0.63671875
5 0.21875 0.85546875
6 0.109375 0.96484375
7 0.03125 0.99609375
8 0.00390625 1.0
From 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) = 0.8555
Note: All answers above have been rounded to the nearest 4 places of decimals.
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