If the quality of individual boards varies according to a normal distribution with mean µ = 100 and standard deviation σ = 4 , what will be the distribution of the sample averages? (Recall the sample size is n = 5.)

The distribution of sample averages will have a normal distribution withe mean = 100 and a stamdard deviation of 1.789.

Step-by-step explanation:

According to the central limit theorem, the mean of the distribution of sample means is equal to the population mean.

μₓ = μ = 100

The theorem goes further to explain that if samples of finite size are obtained from the population, the distribution of sample means will approximate the distribution of the population. Since the population is known to have data that is distributed normally, the distribution of sample means will have a normal distribution too.

The standard deviation of the distribution of sample means is given as the standard error of the mean,

σₓ = (σ/√n)

where σ = population standard deviation = 4

n = sample size = 5

σₓ = (4/√5) = 1.789

Hope this Helps!!!

The answer is, with a  mean 100 and a standard deviation of 4/ root 5.

Step-by-step explanation:

From the given question, let us recall the following,

Normal distribution with µ = 100

The standard deviation σ =4

the sample size n =5

Therefore,

The distribution of x will be normal with the mean 100 and a standard deviation of 4/ root 5,  

Which is denoted as,

Mean 100 = 4√5

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.