Answer:
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!!!
Answer:
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
