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Default Random Numbers with certain numbers more common than others

I need to get a random distribution of numbers to simulate a series of events
that will occur between 44%-72% of the time on a weekly basis over the course
of a year. The high and low ends of this range will occur much less often
than the middle of the range, and I want the random numbers to refelct this.

To explain by example, say a person is flipping a coin, but the coin is
rigged to be heads slightly more often than tails, say on average 55% of the
time. You toss this coin 100 times every week, some weeks it will be heads
56% of the time, others 70% of the time, others 45%. However, most of the
weeks the percentage of heads will be between 50% and 60% of the time, and
less frequently it will be heads in the 44-49% or 61-72% ranges.

Is there a way to set up RANDBETWEEN so that it gives random numbers but
they are weighted to return some numbers more frequently than others, i.e.,
it returns 52-60 70% of the time and 44-51 or 59-72 the remaining 30% of the
time?

Thanks for your help. Hope this wasn't too long.
 
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