Stats question...please help. Thank you!?

Question

According to the Information Please Almanac, 80% of adult smokers started smoking before turning 18 years old.  Suppose 10 smokers 18 years old or older are randomly selected and the number of smokers who started smoking before 18 is recorded.

You must know the following from reading the problem: 
	 n = 10 	p = .8 		
b.	Find the probability that exactly 8 of them started smoking before 18 years of age.

c.	Find the probability that at least 8 of them started smoking before 18 years of age.

d.	Find the probability that fewer than 8 of them started smoking before 18 years of age.

e.	Find the probability that between 7 and 9 of them, inclusive, started smoking before 18 years of age.

Round answers to 4 decimal places

I'm confused so please help me. Thank you very much!

Mathmom · Answer

b.

P(X=x) = (n C x) p^x (1-p)^(n-x) = (10 C x) 0.8^x 0.2^(10-x)

P(X=8) = (10 C 8) * 0.8^8 * 0.2^2 = 0.30199 = 30.2%

--------------------

c.

P(X≥8) = P(X=8) + P(X=9) + P(X=10)
............ = (10 C 8) * 0.8^8 * 0.2^2 + (10 C 9) * 0.8^9 * 0.2 + (10 C 10) * 0.8^10
............ = 0.6778 = 67.78 %

--------------------

d.

P(X<8) = 1 - P(X≥8)
............ = 1 - 0.6778
............ = 0.3222 = 32.22 %

--------------------

e.

P(7≤X≤9) = P(X=7) + P(X=8) + P(X=9)
................. = (10 C 7) * 0.8^7 * 0.2^3 + (10 C 8) * 0.8^8 * 0.2^2 + (10 C 9) * 0.8^9 * 0.2
................. = 0.7718 = 77.18 %

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Stats question...please help. Thank you!?

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