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anonymous
 one year ago
Consider a binomial random variable with n = 9 and p = 0.3. Let x be the number of successes in the sample.
a. Find the probability that x is exactly 2.
b. Find the probability that x is less than 2.
c. Find P(x > 2).
d. Find P(2 ≤ x ≤ 4).
I've solved the a) but I can't get the other 3. I got 0.267 for a).
anonymous
 one year ago
Consider a binomial random variable with n = 9 and p = 0.3. Let x be the number of successes in the sample. a. Find the probability that x is exactly 2. b. Find the probability that x is less than 2. c. Find P(x > 2). d. Find P(2 ≤ x ≤ 4). I've solved the a) but I can't get the other 3. I got 0.267 for a).

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For B, note that P(x < 2) = P(x = 0) + P(x = 1) since these are the only two values the random variable can take below 2.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So do i have to do the same thing i did for part a but repeat it for x = 0 and x = 1?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yep, since you know how to calculate the probability the variable is equal to something you can use that to find the probability it is less than something.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay and for part c i do tht for x = 3 all the way up to 9? that would take forever...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0For part C you can use the fact that P(x > 2) + P(x <= 2) = 1 and use your previous answers to calculate P(x > 2).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Otherwise you're right, it is a bunch of boring calculation :P

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0If something is not larger than 2, then that means it's less than or equal to 2. So P(x > 2) = 1  P(x <= 2). From your first two answers you can calculate P(x <= 2) easily so that's why we do it this way.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Im sorry I still dont get it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's ok, I'm just trying to think of ways to explain it :P Do you know that if you know the probability of something happening then the probability of it not happening is 1 minus that probability?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0btw i think i solved part b is it 0.196?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It is :) So do you agree that P(x > 2) = 1  P(x <= 2)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I dont understand that formula

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It comes from what I said above combined with the fact that is x is not > 2, then it is <= 2.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay that makes sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Alright. So can you find P(x <= 2)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i did c9,1(0.3)^2(0.7)^91 and the same this for 0 to get 0.196

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i used an online calculator to solve it because i dont know how to do it on my calclator

anonymous
 one year ago
Best ResponseYou've already chosen the best response.00.196 is P(x < 2), but you need P(x <= 2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no part b says just less than 2 and i found out how to do it on my calculator had to use the nCr key

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I mean for part C, since we know that P(x > 2) = 1  P(x <= 2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would P(x <=2) be 0.267 + 0.196?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes. Then you can find the answer to C

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so c would be 1  (0.267+0.196)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Wow! thank you I actually understand what you were trying to say earlier

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so how would i go about doing part d?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0is it asking to find x = 3?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well if 2 <= x <= 4 then that means x can be 2, 3, or 4.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right so how can i approach this?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0would i have to solve for x = 2,3,4?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, I think the easiest way to do it here is to just calculate the probabilities for each case and sum them.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0:( okay well atleast I know how to do these srot of questions thank you so much JE!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0No worries, glad I could help! :)
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