Suppose a simple random sample of size nequals41 is obtained from a population with muequals66 and sigmaequals16.(a) what must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean? assuming the normal model can be used, describe the sampling distribution x overbar.

n = 41

According to the central limit theorem

Let is a standard normal variable

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities regarding the sample mean?

Ans. The population must be normally distributed

b) Assuming the normal model can be used, describe the sampling distribution x over bar.

Approximately normal with and

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: