Hello!
Each normal distribution with a mean and standard deviation
may be made standard normal distribution by the linear transformation
where
is any value we are interesting in. Here
(hours) and
(hours).
Then we can use a table of probabilities for a standard normal distribution, I attached the link to it. Note that any normal distribution is symmetric, and the probability of "value less than the mean" is 0.5 (and 0.5, too, for "greater than the mean").
For using with this table, we compute
(- means to the left of the mean).
For we have
The table values for and
are approximately
and
Now we can answer our questions.
1. Less than It is the left half of values with the probability 0.5, and those between 1/2 and
for which we know the probability from the table. So the probability is about
2. Less than It is the left half of values minus those between
and
i.e. the probability is about
. Between
and
It is "between
and
" plus "between
and
", i.e. about
We can use more precise table or online solving tool for the more precise results.
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