answr question 17 and 18 U.S. adults. Find the probability that the number of U.
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answr question 17 and 18
U.S. adults. Find the probability that the number of U.S, adults who that the government should help fight childhood obesity is (a) exactly tow, (b) at least four, and (c) less than three. Ease of Voting Twenty-seven percent of likely U.S. voters think that it is too easy to vote in the United States. You randomly select 12 likely U.S. voters. Find the probability that the number of likely U.S. voters who think that it is too easy to vote in the United States is (a) exactly three, at least four, and less than eight. Junk Food Sixty-three percent of U.S. adults oppose special taxes on junk food and soda. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who oppose special taxes on junk food and soda is exactly six, at least five, and less than eight Clothes Shopping Fifty-six percent of men do not look forward to going clothes shopping for themselves. You randomly select eight men. Find the probability that the number of men who do not look forward to going clothes shopping for themselves is exactly five, more than five, and at most five.Explanation / Answer
17. Voters who think that it is too easy to vote in the United States;(p)= 0.27
Voters who think thatit is not too easy to vote in the United States;(q)= 1-0.27 = 0.73
n=12
(a) The probability that the number of likely U.S. voters who think that it is too easy to vote in the United States is exactly three = P(X=3) = 12c3 * 0.27^3* 0.73^9
= 220 * 0.197 * 0.059
= 0.2549 ~ 0.26 = 26.49%
(b) The probability that the number of likely U.S. voters who think that it is too easy to vote in the United States is at least four = P(X>3)
= 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3)]
= 1 - [(12c0 * 0.27^0* 0.73^12) + (12c1 * 0.27^1* 0.73^11) + (12c2 * 0.27^2* 0.73^10) + (12c3 * 0.27^3* 0.73^9)]
= 1 - [0.0229 + 0.1016 + 0.2068 + 0.2549 ] = 1 - 0.5863
= 0.4137 ~ 0.41 = 41.37%
(c) The probability that the number of likely U.S. voters who think that it is too easy to vote in the United States is less than eight = P(X<8)
= 1 - [P(X=8) + P(X=9) + P(X=10) + P(X=11) + P(X=12)]
= 1 - [(12c8 * 0.27^8* 0.73^4) + (12c9 * 0.27^9* 0.73^3) + (12c10 * 0.27^10* 0.73^2) + (12c11 * 0.27^11* 0.73^1) + (12c12 * 0.27^12* 0.73^0)]
= 1 - [0.00397 + 0.00065 + 0.00007 + 0.00001 + 0.0] = 1 - 0.0047
= 0.9953 ~ 99.53%
18. Adults who oppose special taxes on junk food & soda;(p)= 0.63
Adults who do not oppose special taxes on junk food & soda;(q)= 1-0.63 = 0.37
n=10
(a) The probability that the Adults who oppose special taxes on junk food & soda is exactly six = P(X=6) = 10c6 * 0.63^6* 0.37^4
= 0.246076 ~ 0.2461 = 24.61%
(b) The probability that the Adults who oppose special taxes on junk food & soda is at least five = P(X>4)
= 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4)]
= 1 - [(10c0 * 0.63^0* 0.37^10) + (10c1 * 0.63^1* 0.37^9) + (10c2 * 0.63^2* 0.37^8) + (10c3 * 0.63^3* 0.37^7) + (10c4 * 0.63^4* 0.37^6)]
= 1 - [0.000048 + 0.000819 + 0.006273 + 0.028485 + 0.084877] = 1 - 0.120503
= 0.879497 ~ 0.8795 = 87.95%
(c) The probability that the Adults who oppose special taxes on junk food & soda is less than eight = P(X<8)
= 1 - [P(X=8) + P(X=9) + P(X=10)]
= 1 - [(10c8 * 0.63^8* 0.37^2) + (10c9 * 0.63^9* 0.37^1) + (10c10 * 0.63^10* 0.37^0)]
= 1 - [0.152876 + 0.057845 + 0.009849 ] = 1 - 0.220571
= 0.779429 ~ 0.7794 = 77.94%
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