Please explain how you solved it. It must be done without using software please,

Question

Please explain how you solved it. It must be done without using software please, thank you.

Suppose 50% of the population approves of the job the governor is doing, and that 20 individuals are drawn at random from the population. Solve the following using both the binomial distribution and the normal approximation to the binomial. What is the probability that exactly 7 people will support the governor? What is the probability that 7 or fewer people will support the governor? What is the probability that exactly 11 will support the governor? What is the probability that 11 or fewer will support the governor?

Explanation / Answer

Answer to the following using binomial distribution is as follows:

p = .50

n=20

a. P(X=7) = 20C7(.5^13)*(.5^7) = .074

b. P(X<=7) = 20C0(.5^0)*(.5^20)+....+20C7(.5^13)*(.5^7) = 0.1316

c. P(X=11) =  20C11(.5^11)*(.5^9) = 0.1602

d. P(X<=11) = 20C0(.5^0)*(.5^20)+...+20C11(.5^11)*(.5^9) = 0.7483

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