A sample of 100 independent random numbers is taken from this distribution, and its average is used to estimate the mean of the distribution. What isthe standard error of this estimate?

The standard error in estimating the mean = (0.1 × standard deviation of the distribution)

Step-by-step explanation:

The standard error of the mean, for a sample, σₓ is related to the standard deviation, σ, through the relation

σₓ = σ/(√n)

n = sample size = 100

σₓ = σ/(√100)

σₓ = (σ/10) = 0.1σ

Hence, the standard error in estimating the mean = (0.1 × standard deviation of the distribution)

step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: