Question

According to an​ article, 34​% 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 5 and 7 inclusive.

d. Determine the probability distribution of the random variable X.

Answer 1

The sample size of 9 randomly selected​ adults will have a binomial distribution with parameter n and p. The distribution can be represented as;

The probability distribution for the random variable X is,

a.

For the calculation purpose the probability is obtained in excel using the function =BINOM.DIST(5,9,0.34,FALSE)

For the calculation purpose the probability is obtained in excel using the function =BINOM.DIST(5,9,0.34,FALSE)

For the calculation purpose the probability is obtained in excel using the function =1-BINOM.DIST(4,9,0.34,FALSE)

b.

For the calculation purpose the probability is obtained in excel using the function =1-BINOM.DIST(0,9,0.34,FALSE)

For the calculation purpose the probability is obtained in excel using the function =BINOM.DIST(1,9,0.34,FALSE)

c.

For the calculation purpose the probability is obtained in excel using the function =BINOM.DIST(7,9,0.34,TRUE)-BINOM.DIST(4,9,0.34,TRUE)

d.

The random variable X has following probability distribution

X	P(X=x)
0	0.0238
1	0.1102
2	0.2270
3	0.2729
4	0.2109
5	0.1086
6	0.0373
7	0.0082
8	0.0011
9	0.0001

The probabilities are obtained in excel using the function =BINOM.DIST(x,9,0.34,FALSE) by putting the values of x.