Respuesta :
Answer:
a) [tex]E(X) = 71[/tex]
b)
Variance: [tex]V(X) = 20.59[/tex]
Standard deviation: [tex]\sqrt{V(X)} = 4.58[/tex]
Step-by-step explanation:
For each tweet, there are only two possible outcomes. Either it got a reaction, or it did not. So we use the binomial probability distribution to solve this problem.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The variance of the binomial distribution is:
[tex]V(X) = np(1-p)[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
In this problem, we have that:
[tex]n = 100, p = 0.71[/tex]
a.What is the expected number of these tweets with no reaction?
[tex]E(X) = np = 100*0.71 = 71[/tex]
b.What are the variance and standard deviation for the number of these tweets with no reaction?
Variance:
[tex]V(X) = np(1-p) = 100*0.71*0.29 = 20.59[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.71*0.29} = 4.58[/tex]
