A population of values has a normal distribution with $ \mu = 135.9 $ and $ \sigma = 53.8 $. You intend to draw a random sample of size $ n = 165 $.Find the probability that a single randomly selected value is greater than 140.9.$ P(X > 140.9) = $ [Input box]Find the probability that a sample of size $ n = 165 $ is randomly selected with a mean greater than 140.9.$ P(M > 140.9) = $ [Input box]Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answered: Image /qna-images/answer/560674a0-7c4f-43a9-b94d-35d35b0e36a0.jpg

Answered: A population of values has a normal…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

A population of values has a normal distribution with $ \mu = 135.9 $ and $ \sigma = 53.8 $. You intend to draw a random sample of size $ n = 165 $.

Find the probability that a single randomly selected value is greater than 140.9.

$ P(X > 140.9) = $ [Input box]

Find the probability that a sample of size $ n = 165 $ is randomly selected with a mean greater than 140.9.

$ P(M > 140.9) = $ [Input box]

Enter your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Expert Solution

Step 1: Given data,

$D a t a space f o l l o w s space a space n o r m a l space d i s t r i b u r t i o n comma A space p o p u l a t i o n space m e a n colon mu equals 135.9 A space p o p u l a t i o n space s tan d a r d space d e v i a t i o n colon sigma equals 53.8 A space s a m p l e space s i z e colon n equals 165 W e space h a v e space t o space f i n d space o u t space t h e space p r o b a b i l i t i e s space f o r space t h e space g i v e n space d a t a.$