Respuesta :
Answer:
Mean for a binomial distribution = 374
Standard deviation for a binomial distribution = 12.97
Step-by-step explanation:
We are given a binomial distribution with 680 trials and a probability of success of 0.55.
The above situation can be represented through Binomial distribution;
[tex]P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....[/tex]
where, n = number of trials (samples) taken = 680 trials
r = number of success
p = probability of success which in our question is 0.55
So, it means X ~ [tex]Binom(n=680, p=0.55)[/tex]
Now, we have to find the mean and standard deviation of the given binomial distribution.
- Mean of Binomial Distribution is given by;
E(X) = n [tex]\times[/tex] p
So, E(X) = 680 [tex]\times[/tex] 0.55 = 374
- Standard deviation of Binomial Distribution is given by;
S.D.(X) = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{680 \times 0.55 \times (1-0.55)}[/tex]
= [tex]\sqrt{680 \times 0.55 \times 0.45}[/tex] = 12.97
Therefore, Mean and standard deviation for binomial distribution is 374 and 12.97 respectively.
