Number of different 5 digit combinations if successive digits msut be different
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To find out if a point is inside, on, or outside a circle, we need to substitute the ordered pair into the equation of the circle:
(x-xc)^2+(y-yc)^2=r^2
where (xc,yc) is the centre of the circle, and r=radius of the circle.
If the left-hand side [(x-xc)^2+(y-yc)^2] is less than r^2, then point (x,y) is INSIDE the circle. If the left-hand side is equal to r^2, the point is ON the circle.
Finally, if the left-hand side is greater than r^2, the point is OUTSIDE the circle.
For the given problem, we have xc=3, yc=0, or centre at (3,0), r=sqrt(49)=7
(x-xc)^2+(y-yc)^2=r^2 => (x-3)^2+y^2=7^2
A. (-1,1),
(x-3)^2+y^2=7^2 => (-1-3)^2+1^2=16+1=17 <49 [inside circle]
B. (10,0)
(x-3)^2+y^2=7^2 => (10-3)^2+0^2=49+0=49 [on circle]
C. (4,-8)
(x-3)^2+y^2=7^2 => (4-3)^2+(-8)^2=1+64=65 > 49 [outside circle]
(x-xc)^2+(y-yc)^2=r^2
where (xc,yc) is the centre of the circle, and r=radius of the circle.
If the left-hand side [(x-xc)^2+(y-yc)^2] is less than r^2, then point (x,y) is INSIDE the circle. If the left-hand side is equal to r^2, the point is ON the circle.
Finally, if the left-hand side is greater than r^2, the point is OUTSIDE the circle.
For the given problem, we have xc=3, yc=0, or centre at (3,0), r=sqrt(49)=7
(x-xc)^2+(y-yc)^2=r^2 => (x-3)^2+y^2=7^2
A. (-1,1),
(x-3)^2+y^2=7^2 => (-1-3)^2+1^2=16+1=17 <49 [inside circle]
B. (10,0)
(x-3)^2+y^2=7^2 => (10-3)^2+0^2=49+0=49 [on circle]
C. (4,-8)
(x-3)^2+y^2=7^2 => (4-3)^2+(-8)^2=1+64=65 > 49 [outside circle]
Answer:
(a) The standard error of the mean in this experiment is $0.052.
(b) The probability that the sample mean is between $3.78 and $3.86 is 0.5587.
(c) The probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.
(d) The likelihood that the sample mean is greater than $3.92 is 0.9726.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean <em>μ</em> and standard deviation <em>σ</em> and appropriately huge random samples (<em>n</em> > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.
Then, the mean of the distribution of sample mean is given by,
And the standard deviation of the distribution of sample mean is given by,
The information provided is:
As <em>n</em> = 40 > 30, the distribution of sample mean is .
(a)
The standard error is the standard deviation of the sampling distribution of sample mean.
Compute the standard deviation of the sampling distribution of sample mean as follows:
Thus, the standard error of the mean in this experiment is $0.052.
(b)
Compute the probability that the sample mean is between $3.78 and $3.86 as follows:
Thus, the probability that the sample mean is between $3.78 and $3.86 is 0.5587.
(c)
If the difference between the sample mean and the population mean is less than $0.01 then:
Compute the value of as follows:
Thus, the probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.
(d)
Compute the probability that the sample mean is greater than $3.92 as follows:
Thus, the likelihood that the sample mean is greater than $3.92 is 0.9726.