Answer:
a = and b =
Step-by-step explanation:
As we know, the radius of the unit circle is 1 unit (it is the hypotenuse in the right triangle, the blue line)
We use trigonometric formulas to find out a and b
<=> Sin(45) = b / 1
<=> b= Sin(45)*1 =
<=> Cos(45) = a / 1
<=> a = Cos(45)*1 =
So: a = and b =
Answer:
If we divide both sides by we got:
And we can use the normal distribution table or excel to find the probabilites and 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".
Solution to the problem
Let X the random variable that represent the area of a population, and for this case we know the distribution for X is given by:
Where and
We select a a sample of n =4 and since the distribution for X is normal then we know that the distribution for the sample mean is given by:
And we want to find this probability:
If we divide both sides by we got:
And we can use the normal distribution table or excel to find the probabilites and we got:
