A sample is chosen randomly from a population that can be described by a Normal model. Complete parts a and b below. ​a) What's the sampling distribution model for the sample​ mean? Describe​ shape, center, and spread. Choose the correct answer below.     A. ​Normal, with a center at σnand a standard deviation of μ.   B. ​Normal, with a center at μand a standard deviation of σn.   C. ​Normal, with a center at σand a standard deviation of μn.   D. ​Normal, with a center at μnand a standard deviation of σ.   Part 2 ​b) If a larger sample is​ chosen, what's the effect on this sampling distribution​ model?     A. The standard deviation will be​ smaller, but the center will remain the same.   B. The center will be​ smaller, but the standard deviation will remain the same.   C. The center will be​ larger, but the standard deviation will remain the same.   D. The standard deviation will be​ larger, but the center will remain the same.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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A sample is chosen randomly from a population that can be described by a Normal model. Complete parts a and b below.

​a) What's the sampling distribution model for the sample​ mean? Describe​ shape, center, and spread. Choose the correct answer below.
 
 
A.
​Normal, with a center at σnand a standard deviation of μ.
 
B.
​Normal, with a center at μand a standard deviation of σn.
 
C.
​Normal, with a center at σand a standard deviation of μn.
 
D.
​Normal, with a center at μnand a standard deviation of σ.
 
Part 2
​b) If a larger sample is​ chosen, what's the effect on this sampling distribution​ model?
 
 
A.
The standard deviation will be​ smaller, but the center will remain the same.
 
B.
The center will be​ smaller, but the standard deviation will remain the same.
 
C.
The center will be​ larger, but the standard deviation will remain the same.
 
D.
The standard deviation will be​ larger, but the center will remain the same.
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