According to www.statistia.com, in 2016 the number of children in US families wa

Question

According to www.statistia.com, in 2016 the number of children in US families was reported to be:

                Number of  

                 Children                 Frequency

                        0                      47,415,000

                        1                      14,791,000

                        2                      13,038,000

                        3+                    6,939,000

If you randomly select 16 students from this class, find the probability that: a. Exactly one of them is an only child b. More than one of them is an only child c. How many of the 16 students would you expect to be an only child Note: When calculating probabilities, remember that it is not possible in our population for a student to come from a family with no children.

Explanation / Answer

P(1)=14791000/82183000=0.18 ( two decimal place approximation)

now we use binomial distribution with parameter n=16 and p=0.18 and for

Binomial distribution ,P(X=r)=nCrpr(1-p)n-r  

(a)  probability that Exactly one of them is an only child =P(X=1)=0.1468

( using ms-excel==BINOMDIST(1,16,0.18,0))

(b)probability that More than one of them is an only child=P(X>1)=1-P(X<=1)=1-0.1885=0.8115 ( P(X<=1)=0.1885

( using ms-excel=BINOMDIST(1,16,0.18,1))

(c) expect to be an only child=n*p=16*0.18=2.88 ( nearest whole number is 3)

answer is 3.

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