Question

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

Answer 1

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.