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Suppose X is a Normal random variable with with expected value 3-√3 and standard deviation √3. We take a random sample of size n from the distribution of X. Let X be the sample mean. Use R to determine the following: a) Find the probability P(X> 5.61) b) Find the probability P(X> 5.61) when n = 4 c) Find the probability P(X> 5.61) when n = 16 [ d) Find the probability P( 5 < X < 5.33) when n = 16 [ e) Find the standard deviation of X when n = 16[ f) Find the probability that X₁ + X₂ + ... +X16 < 84.

Suppose X is a Normal random variable with with expected value 3-√3 and standard deviation √3. We take a random sample of size n from the distribution of X. Let X be the sample mean. Use R to determine the following: a) Find the probability P(X> 5.61) b) Find the probability P(X> 5.61) when n = 4 c) Find the probability P(X> 5.61) when n = 16 [ d) Find the probability P( 5 < X < 5.33) when n = 16 [ e) Find the standard deviation of X when n = 16[ f) Find the probability that X₁ + X₂ + ... +X16 < 84.

MATLAB: An Introduction with Applications
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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Suppose X is a Normal random variable with with expected value 3-√3 and standard deviation √3. We take a random sample of size n from the distribution of X. Let X be the sample mean. Use R to determine the following: a) Find the probability P(X> 5.61) b) Find the probability P(X> 5.61) when n = 4 c) Find the probability P(X> 5.61) when n = 16 d) Find the probability P( 5 < X < 5.33) when n = 16 e) Find the standard deviation of X when n = 16 f) Find the probability that X₁ + X₂ + ... +X16 < 84. g) Copy your R script for the above into the text box here.
Transcribed Image Text:Suppose X is a Normal random variable with with expected value 3-√3 and standard deviation √3. We take a random sample of size n from the distribution of X. Let X be the sample mean. Use R to determine the following: a) Find the probability P(X> 5.61) b) Find the probability P(X> 5.61) when n = 4 c) Find the probability P(X> 5.61) when n = 16 d) Find the probability P( 5 < X < 5.33) when n = 16 e) Find the standard deviation of X when n = 16 f) Find the probability that X₁ + X₂ + ... +X16 < 84. g) Copy your R script for the above into the text box here.
Suppose X has normal distribution with mean 0.59 and standard deviation a) What is the expected value of 4X + 3? b) What is the variance of 4X + 3? c) Calculate the probability X > 2.40 | d) Calculate the probability that X < 2.40 e) Calculate the probability that 2.3 < X < 2.5 f) If the probability that X > t = 0.57 then what is t? g) Copy your R script for the above into the text box here. The pnorm(), dnorm() and qnorm() functions should be useful in the following.
Transcribed Image Text:Suppose X has normal distribution with mean 0.59 and standard deviation a) What is the expected value of 4X + 3? b) What is the variance of 4X + 3? c) Calculate the probability X > 2.40 | d) Calculate the probability that X < 2.40 e) Calculate the probability that 2.3 < X < 2.5 f) If the probability that X > t = 0.57 then what is t? g) Copy your R script for the above into the text box here. The pnorm(), dnorm() and qnorm() functions should be useful in the following.
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