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

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mathmate mathmate · Answer 1 · 2019-04-08T12:33:21+02:00

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.