Thirty percent of households say they would feel secure if they had $50,000 in s

Question

Thirty 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. (a) Find the probability that the number that say they would feel secure is exactly five. P(5)= 0.047 (Round to three decimal places as needed.) (b) Find the probability that the number that say they would feel secure is more than five P(x > 5) = (Round to three decimal places as needed.)

Explanation / Answer

(a) Probability of feeling secure p = 0.3

Probability of not feeling secure 1 - p = 0.7

Probability that five will feel secure out of 8 = 8C5 * (0.3)5 * (0.7)3

= 56 * (0.3)5 * (0.7)3

= 0.0467

= 0.047

(b) n = 8 p = 0.3 1 - p = 0.7

Mean = np = 8 * 0.3 = 2.4

Standard deviation = (np(1 - p))

= (2.4*0.7)

= 1.2961

X = 5.5

Z = (X - ) /

= (5.5 - 2.4) / 1.2961

= 2.3918

Probability from table P(Z > 2.3918) = 0.0084.

=> P(X > 5) = 0.0084 = 0.008.

(c) P(X <= 5) = 1 - 0.0084 = 0.9916 = 0.992.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.