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It is hypothesized that the proportion of individuals in a population with type O blood is 0.3. If this hypothesis is correct, what is the the approximate probability that in a random sample of 560, the proportion of blood type O individuals will be less than 0.25 or greater than 0.35? (answer is 0.98%

but I don't know how to get it)

What you're looking for is binomial probability, which tells you the chance of getting X successful outcomes out of Y attempts with probability of success P. You know that P = 0.3, so what you want to find is the probability of getting less than 140 (corresponding to 0.25) or greater than 196 (.35) "successes" out of your 560 attempts. You get answers of .005 and .006 respectively. Then the final answer is the probability of getting neither of these outcomes, which is (1-A)*(1-B), 0.989. It looks like your answer key is just rounding down to 98% instead of up to 99%.


Edit: I'm assuming you mis-typed something and you're looking for the probability that the observed number will fall within the 0.25-0.35 range, not outside of it. No matter how you round the chances of getting a result on the extreme end of the range will be way less than 98%.

Well the answer is 0.98% not 98% so it is way less than 98%, anyways I'll try your idea.


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What formula did you use as I'm still having difficulties.

Unless you are using statistical software you are going to be there forever if you use the binomial distribution. I'd highly recommend using the normal approximation to the binomial. It is much easier for an inconsequential drop in accuracy.