Respuesta :
Answer:
Mean and Standard deviation for the numbers of girls in groups of 36 births are 18 and 3 respectively.
Step-by-step explanation:
We are given that he X SORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.
Now consider a group consisting of 36 couples.
The above situation can be represented through binomial distribution;
[tex]P(X=r)=\binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x=0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 36 couples
r = number of success
p = probability of success which in our question is probability
of a girl, i.e.; p = 0.5
Let X = Numbers of girls in groups of 36 births
So, X ~ Binom(n = 36, p = 0.5)
Now, mean for the numbers of girls in groups of 36 births is given by;
Mean, E(X) = [tex]n \times p[/tex] = [tex]36 \times 0.5[/tex] = 18
Also, standard deviation for the numbers of girls in groups of 36 births is given by;
Standard deviation, S.D.(X) = [tex]\sqrt{n\times p\times (1-p)}[/tex]
= [tex]\sqrt{36\times 0.5\times (1-0.5)}[/tex]
= 3
