SOLUTION: There are dashes over the x's I don't know how to start the equations since I know nothing about algebra since I never took it in school. Suppose that we will randomly select a

Question 483477: There are dashes over the x's I don't know how to start the equations since I know nothing about algebra since I never took it in school.
Suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4.
a. Describe the shape of the sampling distribution of the sample mean �. Do we need to make any assumptions about the shape of the population? Why or why not?
b. Find the mean and the standard deviation of the sampling distribution of the sample mean �.
c. Calculate the probability that we will obtain a sample mean greater than 21; that is, calculate P (� > 21). Hint: Find the z value corresponding to 21 by using �x and ơx because we wish to calculate a probability about x. Then sketch the sampling distribution and the probability.
d. Calculate the probability that we will obtain a sample mean less than 19.385; that is, calculate P (� < 19.385).

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Suppose that we will randomly select a sample of 64 measurements from a population having a mean equal to 20 and a standard deviation equal to 4.
----------------------------------------
a. Describe the shape of the sampling distribution of the sample means �.
Ans: Nearly normal according to the Central Limit theorem.
-------------------------
Do we need to make any assumptions about the shape of the population? Why or why not?
Ans: Check the statement of the Central Limit Theorem in your text.
-------------------------
b. Find the mean and the standard deviation of the sampling distribution of the sample mean �.
mean of the sample means = 20
std of the sample means = 4/sqrt(64) = 1/2
---------------------------------
c. Calculate the probability that we will obtain a sample mean greater than 21; that is, calculate P (x-bar > 21). Hint: Find the z value corresponding to 21 by using �x and ơx because we wish to calculate a probability about x. Then sketch the sampling distribution and the probability.
z(21) = (21-20)/[1/2] = 2
---
P(x-bar > 21) = P(z > 2) = 0.0228
----------------------------------
d. Calculate the probability that we will obtain a sample mean less than 19.385; that is,
calculate P (x-bar < 19.385)
----
z(19.385) = (19.385-21)/(1/2) = -3.2300
---
P(x-bar < 19.385) = P(z < -3.2300) = 0.00061901
==================
Cheers,
Stan H.
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