5.6.181 Acco ng to an anes 47% o ada s have experienced a breakup at i ast once

Question

5.6.181 Acco ng to an anes 47% o ada s have experienced a breakup at i ast once during the last 10 years or 9 rand ty selected aduits, find the pro abilty mat the number, who have expervenced a breakup at least once during the last 10 years is a. exactly tive, at most five, at least five b. at least one, at most one d. Determine the probability distribution of the random variable X The probably eat exactly tve adun have exper enced a breakup at least once during the last 10 years is [ (Round to four doonal places as needed) Enter your answer in the answer box and then click Check Anwer 6 6 O.

Explanation / Answer

p = 0.47

a)
Exactly five
P(X = 5) = 0.2280
=BINOM.DIST(5,9,0.47,FALSE)

At most 5
P(X <= 5) = 0.8015
=BINOM.DIST(5,9,0.47,TRUE)

At least 5
P(X >=5) = 0.4265
=1-BINOM.DIST(4,9,0.47,TRUE)

b)
At least 1
P(X >= 1) = 1 - P(X = 0)
= 1 - (1-0.47)^9
= 0.9967
=1-BINOM.DIST(0,9,0.47,TRUE)

At most 1
P(X <= 1) = P(X=0) + P(X=1)
= (1-0.47)^9 + 9*0.47*0.53^8
= 0.0296
=BINOM.DIST(1,9,0.47,TRUE)

c)
between four and six, inclusive
P(4<=X<=6) = p(X=4) + P(X=5) + P(X=6)
= 9C4*0.47^4*0.53^5 + 9C5*0.47^5*0.53^4 + 9C6*0.47^6*0.53^3
= 0.6199
=BINOM.DIST(6,9,0.47,TRUE) - BINOM.DIST(3,9,0.47,TRUE)

d)
This is binomial distribution

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