Question

According to an​ article, 36% of adults have experienced a breakup at least once during the last 10 years. Of 9 randomly selected​ adults, find the probability that the​ number, X, who have experienced a breakup at least once during the last 10 years is

a. exactly​ five; at most​ five; at least five.

b. at least​ one; at most one.

c. between five and seven​, inclusive.

d. Determine the probability distribution of the variables X. (X=0-9)

Answer 1

Here p=0.36 which is same for all, n=9 is constant, events are independent and only two outcomes

Hence all the properties of binomial are satisfied

So we will use excel formula of binomial distribution to find required probabilities

a.

P(x = 5) = BINOM DIST(5,9, 0.36,0) = 0.1278

Par <5) = BINOM DIST(5,9, 0.36,1) = 0.9388

Plz > 5) = 1-Plx<5) = 1-P.1 < 4) = 1-BINOMDI ST(4,9, 0.36,1) = 1 – 0.8110 = 0.189

b.

Plz > 1) = 1-P1 <1) = 1-P1 <0) = 1-BINOMDIST(0,9, 0.36,1) = 1- 0.018 = 0.9820

P(< 1) = BINOM DIST(1,9, 0.36,1) = 0.1092

c.

P(5<7 < 7) = P1 < 7) - P(Z < 4) = BINOM DIST(7,9,0.36,1) – BINOMDIST(4.9.0.36, 1) = 0.9983 – 0.8110 = 0.1873

d.

x	P(x)=BINOMDIST(x,n,p,0)
0	0.0180
1	0.0912
2	0.2052
3	0.2693
4	0.2272
5	0.1278
6	0.0479
7	0.0116
8	0.0016
9	0.0001

It is binomial distribution with p=0.36 and n=9