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Normal Distribution :(

Here's the question

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 :facepalm2: I tried to approximate to the Poisson distribution, but the mean was wayyyyyyyy too large

Help for rep! :smile:
Reply 1
Avatar for Pheylan
Pheylan
isn't it 0? because the normal distribution is continuous... i'm probably wrong
V1NY
Here's the question

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 :facepalm2: I tried to approximate to the Poisson distribution, but the mean was wayyyyyyyy too large

Help for rep! :smile:


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.
Reply 3
Avatar for V1NY
V1NY
OP
1
But the answer is 0.025 :confused:
V1NY
But the answer is 0.025 :confused:

I'll just try it out, hold up.
Reply 5
Avatar for Sub Zero
Sub Zero
1
V1NY
But the answer is 0.025 :confused:


continuity correction?
it could be 104.5< X < 105.5
that's all i can think of other than putting it as binomial
Sub Zero
continuity correction?
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 :p:
Reply 7
Avatar for miml
miml
17
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
Is there an N is this question?
V1NY
But the answer is 0.025 :confused:


Because of this: 'The scores are reported to the nearest integer.'

This means that exactly P(X=105) is:

P(X<105.5)−P(X≤104.5) P(X < 105.5) - P (X \leq 104.5)

Usually, finding an exact value with the normal distribution is zero as I explained earlier.
Reply 10
Avatar for V1NY
V1NY
OP
1
Clarity Incognito
Because of this: 'The scores are reported to the nearest integer.'

This means that exactly P(X=105) is:

P(X<105.5)−P(X≤104.5) P(X < 105.5) - P (X \leq 104.5)

Usually, finding an exact value with the normal distribution is zero as I explained earlier.


I seeeeeeeee, thank you! rep for you :smile:
V1NY
I seeeeeeeee, thank you! rep for you :smile:


No worries et merci beaucoup!

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