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Stats 1: Binomial distribution

Hi,

My book explains an answer but I don't understand the explanation. The question is out of 20 people who are asked a question with a yes or no answer, answering 'yes' has a 0.6 probability. What is the probability that 10 or more will answer yes?

So this is how the book explains it: P(yes) = 0.6, which is too big for the tables, so use P(no) = 0.4. OK, this bit is clear.

Then it says, P(≥10 \geq 10 say yes) = P(≤10 \leq 10 say no). This is the bit I don't understand. My thought was that people saying no should be equal to or less than 9, as the '10' is being used in the 'yes'. It seems to me as though the 10 is being used twice....I know I'm expressing myself really clumsily but I'm not sure how else to describe it. Could someone explain to me why it is that for the 'no' answers we still use equal to or less than 10?
Reply 1
Avatar for Matt85259
Matt85259
Think about it this way. If 10 of 20 people say no, then 10 must have said yes, meeting the criteria set out.
Reply 2
Avatar for gavinlee
gavinlee
OP
Thanks....sometimes it's the most obvious things that aren't considered! :wink:
Reply 3
Avatar for Matt85259
Matt85259
Indeed! It's quite normal to question something like that when it comes to inequalities as it often is the case that it doesn't make sense.

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