M17 Binomial Distribution Video Lecture | Mintab Tutorials for Beginners - Data & Analytics

we're going to use Minitab to calculate
some things related to the binomial
distribution so here you can see I've
got a series of questions for you on New
Year's Day twelve babies were born at
women's and babies Hospital what's the
probability that three of them were
girls what's the probability that six of
them were girls and so on I have more
questions of that nature what I want to
know is the probabilities of all these
things that are being asked for so I'm
gonna find out a probability
distribution for the variable the
variable is the number of girls that
were born so in column one let me call
this girls and now think about this with
me if there are 12 babies born at
women's and babies Hospital what's the
fewest number of girls you could get 0
of course right what's the most you
could get 12 and you could get any
number in between so I want to do 0 1 2
3 4 5 6 7 8 9 10 11 and 12 what everyone
agree you can't get any other number of
girls than that if the 12 babies are
born anywhere between 0 and 12 of them
are girls I also want to know what's the
probability of 0 girls what's the
probability of one girl if I knew all
this I could answer all of these
questions so I'm going to make another
column called P of girls probability of
that number of girls occurring now how
am I going to figure out those
probabilities well I can figure it out
because I know what kind of distribution
this is this is babies being born I'm
counting how many of them are girls
counting as a big hint I wonder if this
is a binomial distribution so I ask
myself are these multiple independent
trials yes each one of those babies is
born and shouldn't affect the births of
the other babies what gender those
babies are are we counting successes
yes we're counting numbers of girls and
girls will be our successes so this is a
binomial distribution do I know the
probability of success on a single trial
what's the probability that a baby is
born a girl well we're assuming boys and
girls are equally likely so that should
be 50% or 0.5 as the probability so now
I am ready to make Minitab calculate
these things right here because I have
identified for myself when something is
binomial don't worry I clicked on the
session window and it hid part of the
worksheet but I can get the work
back in a second we identified that n is
equal to 12 because we have 12
independent trials and P is equal to 0.5
and if we wanted we would also know what
Q is and Q the probability of a failure
or of a boy is also 0.5 all right
excellent so now I'll click this make it
come back let's go to calculate that so
I'm going to go here to calc and I'm
going to probability distribution so I'm
calculating a probability distribution
in this case a binomial distribution so
I want to find the one that says
binomial right there sixth one down
binomial how click on it and Minitab
opens up a dialog box and it wants to
know a few things so I either want a
probability or accumulative probability
if in this case I want a probability I
want to know the probability of 0 the
probability of 1 the probability of 2
what a cumulative probability would do
is it would add as you go so this first
one would be the probability of 0 the
second one would be the probability of 0
or 1 the third one would be the
probability of 0 or 1 or 2 the third or
the next one would be the probability of
0 or 1 or 2 or 3 it would add as it goes
so this last one would certainly be a 1
I don't want cumulative probability I
want probability number of trials well
we've said there are 12 independent
trials each baby is an independent trial
and the event probability is 0.5 the
probability of a success on a single
trial is 0.5 now I want to know where's
my input coming from well my input is
these numbers 0 through 12 so it's this
column c1 girl so I'm going to click in
here and it gives me choices c1 girls
and it says do you want me to store the
answer somewhere yes please will you
store it in column C to P of girls so
I'll double click P of girls to put that
there and say okay and Minitab
calculates all of these different values
for me so now let's see if we can answer
the questions that were asked what is
the probability that 3 of them are girls
oh that's awkward here let me move this
up so that I can still see there we go
what's the probability that 3 of them
were girls I will look right here where
there was three girls that probability
was point zero five three seven one
one so 0.05 3/7 about 5.4 percent right
what's the probability that six of them
were girls I'll look right here where
the six was six is 0.2 two five five
eight six so we'll say zero point two
two five six so twenty two point six
percent approximately what's the
probability that ten of them were girls
I look at where there were ten girls
right here it's about one point six
percent zero point zero one six one and
now what's the probability that at least
ten of them were girls
I wrote ten of there whoops I'm at ten
of them what's the probability that at
least ten of them were girls that would
be 10 or more 10 or 11 or 12 I'm going
to want to add those up it's going to be
zero point zero one six one plus zero
point zero zero two nine plus zero point
zero zero zero two and so on I'd have to
get out a calculator and add those up
here I'll do that for you real quick but
it's going to be about what one point
eight percent one point nine percent
something like that let's see point zero
one six one plus point zero zero to nine
plus point zero zero zero two and we get
yeah zero point zero one nine two or 1.9
percent whoops I was supposed to put an
equal sign in there sorry about that
how's that Oh zero I must have hit my
insert keys all right zero point zero
one nine too
I was having trouble with that but there
I got it in there now there we go
that is the answers to all those
questions using Minitab to find the
binomial distribution