2323% of a certain country\'s voters think that it is too easy to vote in their

Question

2323%
of a certain country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is (a) exactly three, (b) at least four, (c) less than eight.
(a)
Upper P left parenthesis 3 right parenthesis equals nothingP(3)=
(Round to three decimal places as needed.)
(b)
Upper P left parenthesis x greater than or equals 4 right parenthesis equals nothingP(x4)=
(Round to three decimal places as needed.)
(c)
Upper P left parenthesis x less than 8 right parenthesis equals nothingP(x<8)=

Explanation / Answer

p = 0.23

n = 12

P(X = x) = 12Cx * 0.23x * (1-0.23)12-x

A)P(X = 3) = 12C3 * 0.233 * 0.779 = 0.2547

B) P(X > 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3))

= 1 - (12C0 * 0.230 * 0.7712 + 12C1 * 0.231 * 0.7711 + 12C2 * 0.232 * 0.7710 + 12C3 * 0.233 * 0.779)

= 1 - 0.7096

= 0.2904

C) P(X < 8) = 1 - (P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12))

= 1 - (12C8 * 0.238 * 0.774 + 12C9 * 0.239 * 0.773 + 12C10 * 0.2310 * 0.772 + 12C11 * 0.2311 * 0.771 + 12C12 * 0.2312 * 0.770)

= 1 - 0.0016

= 0.9984

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

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