How to prove two equations have infinite solutions?
1 answer:
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Let 
denote the random variable representing a given number in the total set of numbers. We're told that 
of the numbers fall within a given range, so we know
where is normally distributed with mean 45 and an unknown variance 
.
Let's make the transformation to a random variable with a standard normal distribution:
Since
is symmetric, we have
The mean of is 0, and by symmetry we know that exactly half of the distribution falls to the left of 
, so 
. We're left with
This probability corresponds to a value of
, which means
where
Let's make the transformation to a random variable with a standard normal distribution:
Since
The mean of
This probability corresponds to a value of