Respuesta :
Answer:
a) 600
b) 18.97
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they support the increase, or they do not. The probability of an adult supporting the increase is independent of other adults. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Sample of 1500 adults
So [tex]n = 1500[/tex]
Suppose that 40% of all adults in Ohio support the increase.
This means that [tex]p = 0.4[/tex]
a. The mean of X is:
[tex]E(X) = np = 1500*0.4 = 600[/tex]
b.The standard deviation of X is?
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{1500*0.4*0.6} = 18.97[/tex]
