Answer:
For the sampling distribution,
a) Mean = μₓ = 55.0 students.
b) Standard Deviation = 1.8 students.
Step-by-step explanation:
The complete Question is attached to this solution.
The Central limit theorem explains that for the sampling distribution, the mean is approximately equal to the population mean and the standard deviation of the sampling distribution is related to the population standard deviation through
σₓ = (σ/√n)
where σ = population standard deviation = 4
n = sample size = 5
Mean = population mean
μₓ = μ = 55 students.
Standard deviation
σₓ = (σ/√n) = (4/√5) = 1.789 students = 1.8 students to 1 d.p
Hope this Helps!!!
Answer:
Step-by-step explanation:
step 1
Find the area of complete circle
The area of the circle is given by the formula
we have
substitute
step 2
Find the area of the shaded region
we know that
The area of complete circle subtends a central angle of 360 degrees
so
using proportion
Find out the area of the shaded region if the central angle is equal to 80 degrees
It looks like you're given
Then by the additivity of definite integrals this is the same as
(presumably this is what the hint suggests to use)
Then by the fundamental theorem of calculus, we have