Eighty 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 exactly five, (b) more than five, and (c) at most five c.) Find the probability that the number that say they would feel secure is at most five. P(&lt;5)= (round to three decimal places as needed).

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Eighty 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 exactly five, (b) more than five, and (c) at most five c.) Find the probability that the number that say they would feel secure is at most five. P(&amp;lt;5)= (round to three decimal places as needed).

wheezym · Accepted Answer

Step 1 Given data Probability of households feeling insecure p=0.80 n=8 a) probability that the number that say they would feel secure is exactly five is given by Applying Binomial theorem Probability of x success out of n trial is given by P(X=x)=(nx)×px×(1−p)n−x ⇒P(X=5)=(85)×0.85×(1−0.8)8−5 =8!5!×(8−5)!×0.85×(1−0.8)8−5 =0.1468 Step 2 b) probability that the number that say they would feel secure is more than five is given by Applying Binomial theorem Probability of x success out of n trial is given by P(X=x)=(nx)×px×(1−p)n−x ⇒P(X&amp;gt;5)=P(X=6)+P(X=7)+P(X=8) ⇒(86)×0.86×(1−0.8)8−6+(87)×0.87×(1−0.8)8−7+(88)×(1−0.8)8−8 ⇒0.294+0.336+0.168 =0.797 Step 3 c) probability that the number that say they would feel secure is at most five is given by Applying Binomial theorem Probability of x success out of n trial is given by P(X=x)=(nx)×px×(1−p)n−x ⇒P(X≤5)=1−P(X&amp;gt;5) ⇒1−0.797 =0.203 Step 4 Answer a) probability that the number that say they would feel secure is exactly five is 0.1468 b) probability that the number that say they would feel secure is more than five is 0.797 c) probability that the number that say they would feel secure is at most five is 0.203

Eighty percent of households say they would feel secure if they had 50,000 in sa

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