C. At least 3 were unemployedd. Fewer than 2 were unemployed.Source: U.S. Department of Justice.14. Destination Weddings Twenty-six percent of coupleswho plan to marry this year are planning destinationweddings. Ina random sample of 12 couples who planto marry, find the probability thata. Exactly 6 couples will have a destination weddingb. At least 6 couples will have a destination weddingC. Fewer than 5 couples will have a destination wed-ding00$us2 E 11Source: Time magazine.15. People Who Have Some College Education Fifty-

Question
Asked Oct 15, 2019

Hello, I am studying for an exam. I'm not sure how to tackle this problem and I cant find any examples in my textbook or notes. Any help would be awesome. Thank you.

Sample question 14 is the one I am seeking clarification on. 

 

C. At least 3 were unemployed
d. Fewer than 2 were unemployed.
Source: U.S. Department of Justice.
14. Destination Weddings Twenty-six percent of couples
who plan to marry this year are planning destination
weddings. Ina random sample of 12 couples who plan
to marry, find the probability that
a. Exactly 6 couples will have a destination wedding
b. At least 6 couples will have a destination wedding
C. Fewer than 5 couples will have a destination wed-
ding
00$
us2 E 11
Source: Time magazine.
15. People Who Have Some College Education Fifty-
help_outline

Image Transcriptionclose

C. At least 3 were unemployed d. Fewer than 2 were unemployed. Source: U.S. Department of Justice. 14. Destination Weddings Twenty-six percent of couples who plan to marry this year are planning destination weddings. Ina random sample of 12 couples who plan to marry, find the probability that a. Exactly 6 couples will have a destination wedding b. At least 6 couples will have a destination wedding C. Fewer than 5 couples will have a destination wed- ding 00$ us2 E 11 Source: Time magazine. 15. People Who Have Some College Education Fifty-

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check_circleExpert Solution
Step 1

Consider a random variable X which, follows binomial distribution, indicates the number of couples who are planning destination weddings.

According to the provided data, the number of trials, n is 12 and the probability, p of planning destination weddings is 0.26.

The binomial distribution formula is used here,

P(Xx) "C,p (1-p)"
n-x
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P(Xx) "C,p (1-p)" n-x

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Step 2

a. The probability of exactly 6 couples will have a destination wedding is,

P(X 6)"C, (0.26) (1-0.26)4
924x0.0000507259
= 0.0468
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P(X 6)"C, (0.26) (1-0.26)4 924x0.0000507259 = 0.0468

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Step 3

b. The probability of at least 6 couples w...

P(X26)=1-P(X<6)
P(X5)+P(X 4) + P(X =3)
= 1-
+P(X 2)+ P(X1)+ P (X = 0),
"C,(0.26 (1-0.26)"C(0.26) (1-0.26
1-C, (0.26) (1-0.26)C, (0.26) (1-0.26)
+"C(0.26) (1-0.26C(0.26) (1-0.26)
12-5
12-4
12-3
12-
12-0
1-(0.1143+0.2034
0.2572+0.2196+ 0.1136+ 0.0269)
=1-0.935
= 0.065
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P(X26)=1-P(X<6) P(X5)+P(X 4) + P(X =3) = 1- +P(X 2)+ P(X1)+ P (X = 0), "C,(0.26 (1-0.26)"C(0.26) (1-0.26 1-C, (0.26) (1-0.26)C, (0.26) (1-0.26) +"C(0.26) (1-0.26C(0.26) (1-0.26) 12-5 12-4 12-3 12- 12-0 1-(0.1143+0.2034 0.2572+0.2196+ 0.1136+ 0.0269) =1-0.935 = 0.065

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