SOLUTION: If the mean of a normal distribution is 25, and the standard deviation is 1, it is highly unlikely that a value in the data is 24.
t or f
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Question 472558: If the mean of a normal distribution is 25, and the standard deviation is 1, it is highly unlikely that a value in the data is 24.
t or f
Found 2 solutions by solver91311, robertb:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
It depends. What sort of data are we talking about? If the data is discrete integer counts, then roughly 25% of your data with the mean and standard deviation parameters given is 24. But if it is measurement data, then out of several Monte Carlo trials of 5000 random numbers normally distributed around 25 with a standard deviation of 1, I obtained zero instances of a data point that was within 6 decimal places of 24. On the other hand, if you consider a measurement stated as 24 somethings (without a decimal fraction specification) you are really only guaranteeing that the measurement is in the range 
. Using that criteria, the count is back up to roughly 25%.
John
My calculator said it, I believe it, that settles it
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Your problem needs restatement. When you are dealing with CONTINUOUS probability function (or pdf), in this case a normal distribution, it doesn't really make sense to ask for the probability of occurence of a PARTICULAR value of the random variable. It will always be ZERO. Probability for continuous random variables always goes one way or the other, and it is always considered cumulatively. (Say "how likely is it for a value to be LESS THAN OR EQUAL TO 24?", or the other way.)
So a direct answer to your question is, TRUE, it is highly unlikely, because its probability is 0.
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