It is difficult to balance our body when we accidentally step on a peel of Banana explain why?
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When we walk on the ground, our foot pushes the ground in the backward direction(action), on the other hand, ground wishes our foot in the forward Direction(reaction). This reaction of ground helps us to move in the forward direction. But when our foot falls on the peel of Banana, then our foot slips on a peel of banana and cannot push the ground in the backward direction so, no reaction force acts on a body. Hence, we lose the balance and fall down.
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Answer:
The 95% confidence interval is given by (3.61;4.39)
Step-by-step explanation:
Notation and definitions
n=15 represent the sample size
represent the sample mean
represent the sample standard deviation
m represent the margin of error
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
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".
Calculate the critical value tc
In order to find the critical value is important to mention that we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. The degrees of freedom are given by:
We can find the critical values in excel using the following formulas:
"=T.INV(0.025,14)" for
"=T.INV(1-0.025,14)" for
The critical value
Calculate the margin of error (m)
The margin of error for the sample mean is given by this formula:
Calculate the confidence interval
The interval for the mean is given by this formula:
And calculating the limits we got:
The 95% confidence interval is given by (3.61;4.39)
Let n and d represent the numerator and denominator of the fraction.
.. (n +1)/(d +1) = 4/5
.. (n -5)/(d -5) = 1/2
Eliminating fractions from these equations gives
.. 5(n +1) = 4(d +1)
.. 2(n -5) = (d -5)
Subtracting the first equation from 4 times the second gives
.. 4(2(n -5)) -(5(n +1)) = 4(d -5) -(4(d +1))
.. 8n -40 -5n -5 = 4d -20 -4d -4
.. 3n = 21
.. n = 7
.. 2(7 -5) = d -5
.. 9 = d
The fraction is 7/9.
.. (n +1)/(d +1) = 4/5
.. (n -5)/(d -5) = 1/2
Eliminating fractions from these equations gives
.. 5(n +1) = 4(d +1)
.. 2(n -5) = (d -5)
Subtracting the first equation from 4 times the second gives
.. 4(2(n -5)) -(5(n +1)) = 4(d -5) -(4(d +1))
.. 8n -40 -5n -5 = 4d -20 -4d -4
.. 3n = 21
.. n = 7
.. 2(7 -5) = d -5
.. 9 = d
The fraction is 7/9.