Answered: sume the random variable has a mean of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Assume the random variable has a mean of 30 and a standard deviation of 6. Consider taking repeated random samples of 30 observations from the random variable and calculating the mean, , for each sample. Calculate the probability that is less than 31

Expert Solution

Step 1: Given data,

$A space p o p u l a t i o n space m e a n colon mu equals 30 A space p o p u l a t i o n space s t a n d a r d space d e v i a t i o n colon sigma equals 6 A space s a m p l e space s i z e colon n equals 30 H e r e space space n greater or equal than 30 comma S o space a s space p e r space C L T space left parenthesis c e n t r a l space l i m i t space t h e o r e m right parenthesis space w e space c a n space u s e space n o r m a l space a p p r o x i m a t i o n space f o r space s a m p l i n g space d i s t r i b u t i o n. space T h e space p r o b a b i l i t y space t h a t space space a space s a m p l e space m e a n space space i s space l e s s space t h a n space 31 space i s space equals ?$