I need some help with binomial theorems. can anyone help solve this?
2 answers:
now, how the heck do we get the coefficient for the term, those 84, 126, 9 and so on?
well, you grab the current coefficient, multiply it times the exponent of the first component,
whatever product you get,
divide it by the exponent of the second component in the "next" term
which will be, whatever the current is +1
for example, how the heck did we get 36 for the 3rd term?
well, the second term has 9 as coefficient, the first component on the second term has an exponent of 8
9 * 8 = 72
the second component, has an exponent of 1, we add one 1 + 1, is the next exponent of it, or the exponent on the next term, thus
(9 * 8)/2 = 36
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Answer:
a)
And we can find this probability like this:
b)
And using the z score we got:
c)
And if we use the continuity correction we got:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Continuity correction means that we need to add and subtract 0.5 before standardizing the value specified.
Part a
Let X the random variable that represent the variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
Part a
For this case we want to find this probability:
And if we use the z score given by:
We got this:
And we can find this probability like this:
Part b
For this case we want this probability:
And if we use the continuity correction we got:
And using the z score we got:
Part c
For this case we want this probability:
And if we use the continuity correction we got: