Birthweights are distributed Normally, with a mean of 3.39kg and a standard deviation of 0.55kg.  What is the probability that a randomly selected sample of 40 newborns will have an average weight of less than 3.45 kg?

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question

Birthweights are distributed Normally, with a mean of 3.39kg and a standard deviation of 0.55kg. 

What is the probability that a randomly selected sample of 40 newborns will have an average weight of less than 3.45 kg? 

Expert Solution
Step 1

Central Limit Theorem for mean:

If a random sample of size n is taken from a population having mean  and standard deviation  then, as the sample size increases, the sample mean approaches the normal distribution with mean  and standard deviation σ/ sqrt(n).

By central limit theorem, the mean of the sampling distribution is μx-bar = 3.39.

The population standard deviation is, σ =0.55. The sample size is, n = 40.

The standard deviation using central limit theorem is σ/√n= 0.55/√40 = 0.08696.

Thus, the sampling distribution of the sample mean(x-bar) for sample of size 40 follows approximately normal distribution with mean μx-bar = 3.39 and standard deviation 0.08696.

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Knowledge Booster
Point Estimation, Limit Theorems, Approximations, and Bounds
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman