Question

In a survey of 1010 married adults, the participants were asked the question: Was a good credit score important when choosing your spouse? Four hundred and ninety-five answered in the affirmative, while 515 answered in the negative. If 6 of those surveyed were selected at random, what is the probability of the following?† (Round your answers to four decimal places.)

(a)

None answered in the affirmative?

(b)

Exactly 4 answered in the affirmative?

(c)

More than 4 answered in the affirmative?

(d)

At least 1 answered in the affirmative?

Answer 1

sol: Given that :- In a survey of 1010 married adults while 515 auswered in the negative If 6 of those surveyed were selected at saudou. out of 1010, 495 adults auswered affirmative so P = 495/1010 - 0.99 Raudom sample of size n=6 were selected at random Let x be the number of adults who auswered affirmative x 8 follows Binomial distribution with n=6 & P=0.99 we have to find P(x=0) P(X=0) = (0,6, 0.49,0) = 0.0176 (:. By using Binomial The probability that noue distribution calculator) auswered in the affirmative is 0.0176

we have to find P(x=4) P(x=4) = (4, 6, 0.49,0) (By using = 0.2249 . Binomial distribution caleulator) The probability that exactly. 4 answered in the affirmative is to. 2249 we have to find P(x74) P(x34) = 1- P(x-4) P(x64) =(4,6, 0.49, 1) (By using Binomial = 0.899721 distribution calculator) So, P(x>4) = 1-0.899721 = 0.1003 The probability that more than 4 auswered in the affirmative is 10.1003] we have to find P(X=1) P(X21) = 1- P(x=0) From part a, p(x=0) = 0.0196 so, p(121) = 1- 0.0176 = 0.9824 The probability that at least I auswered in the affirmative is [0.9824)