Answer:
And we can find this probability with this difference:
And we can find the real value with the following excel code using the binomial distribution:
"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"
And we got 0.118 a very close value from the value obtained using the normal approximation
Step-by-step explanation:
Previous concepts
The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".
Let X the random variable of interest, on this case we now that:
The probability mass function for the Binomial distribution is given as:
Where (nCx) means combinatory and it's given by this formula:
We need to check the conditions in order to use the normal approximation.
So we see that we satisfy the conditions and then we can apply the approximation.
If we appply the approximation the new mean and standard deviation are:
So then we can approximate the random variable as
And we want this probability:
We can use the z score formula given by:
And replacing we got:
And we can find this probability with this difference:
And we can find the real value with the following excel code using the binomial distribution:
"=BINOM.DIST(110,400,0.2,TRUE)-BINOM.DIST(89,400,0.2,TRUE)"
And we got 0.118 a very close value from the value obtained using the normal approximation
Step-by-step explanation:
A leap year occurs every 4th year.
So, 1875 - 1700 = 175
Now let us divide 175 by 4
So, 43 leap years occur between the years 1700 and 1875.
First of all, a bit of theory: since the area of a square is given by
where s is the length of the square. So, if we invert this function we have
.
Moreover, the diagonal of a square cuts the square in two isosceles right triangles, whose legs are the sides, so the diagonal is the hypothenuse and it can be found by
So, the diagonal is the side length, multiplied by the square root of 2.
With that being said, your function could be something like this:
double diagonalFromArea(double area) {
double side = Math.sqrt(area);
double diagonal = side * Math.sqrt(2);
return diagonal;
}