Answer:
a)
b) From the central limit theorem we know that the distribution for the sample mean is given by:
c)
Step-by-step explanation:
Let X the random variable the represent the scores for the test analyzed. We know that:
And we select a sample size of 64.
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Part a
For this case the mean and standard error for the sample mean would be given by:
Part b
From the central limit theorem we know that the distribution for the sample mean is given by:
Part c
For this case we want this probability:
And we can use the z score defined as:
And using this we got:
And using a calculator, excel or the normal standard table we have that:
Answer:
The slope of FG is -1
Step-by-step explanation:
Given
Square EFGH
EF:
Required
Determine the slope of FG
First, we calculate the slope of EF
Make y the subject
The general equation has the form:
Where
Compare to
<em>From the name of the square EFGH, we can conclude that EF and FG are perpendicular</em>
<em />
The relationship between perpendicular lines is:
Where
-- Slope of EF
and
m2 = slope of FG
Substitute 1 for m1 in
<em>Hence, the slope of FG is -1</em>
Answer:
28pi cubic inches The volume of the cone is one-third the volume of the cylinder
Step-by-step explanation:
Use the formulas
Volume of cone = (1/3)* π r^2 * h
Volume of cylinder= π r^2 * h = 84 pi cubic inches
Volume of cone = (1/3) * volume of cylinder = (1/3) * 84 * pi = 28 pi cubic inches
Answer:
HTML and SQL
Step-by-step explanation: