What is the probability a sample of 71 test takers will provide a sample mean test score within 10 points of the population mean of 533 on the Evidence-based Reading and Writing part of the test?

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.

pi x^2

step-by-step explanation:

pi times x squared