Scores on an IQ test are modelled by the Normal distribution with mean 100 and standard deviation 15. The scores are reported to the nearest integer.
Find the probability that a person chosen at random scores
a) Exactly 105
I am actually stumped I tried to approximate to the Poisson distribution, but the mean was wayyyyyyyy too large
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It's a normal distribution and so it is used to approximate the probability of something being more or less than a certain value. The probability that it is exactly one number is zero. It's continuous, doesn't have probabilities for discrete values.
(Original post by Sub Zero)
it could be 104.5< X < 105.5
that's all i can think of other than putting it as binomial
Problem with that is that you use a half continuity correction when approximating the binomial distrubition by a normal distribution, not the other way around. It's put there to take into account of the fact that the normal distribution is continuous. I think it's to do with the fact that 'The scores are reported to the nearest integer.'
EDIT: I just realised that you're correct but with the wrong reasoning
I'd agree with 0, but I'm a bit confused by the question? Does it mean a score of exactly 105 is achieved, or does it mean a score of exactly 105 is reported? Because if it is the latter than we are looking for the probability of the score being between 104.5 and 105.5