Answer:
In this case, sample size is greater than 30,
That is 71 > 30
Therefore, sampling distribution of sample mean x is approximately normal with:
µ = 533 and ∂ = 10.
Step-by-step explanation:
Solution:
Given:
The population standard deviation of ∂ = 100
The probability distribution of all the possible values of sample mean x is termed as sampling distribution of x.
The expected value is E(x) =µ,
µ represent population mean.
µ = 533
The standard deviation is = ∂ /√n
S.D = 100 / √71
= 11.868
For simple random sample of size n drawn from population, the sampling distribution of sample mean x is approximately normal when sample size is greater than or equal to 30.
In this case, sample size is greater than 30,
That is 71 > 30
Therefore, sampling distribution of sample mean x is approximately normal with:
µ = 533 and ∂ = 10.
