Suppose X is a Normal random variable with with expected value 5 and standard deviation 5. 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< 4.0) 0.03593032x b) Find the probability P(X < 4) when n = 9 3.332045e-0 X c) Find the probability P(X < 4) when n = 36 1.721018e-2 x

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I am having trouble with this question and not sure if I am doing it right. I am using the r progaming language for this task

Suppose X is a Normal random variable with with expected value 5 and standard deviation 5. 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< 4.0) 0.03593032 X
b) Find the probability P(X < 4) when n = 9 3.332045e-0X
c) Find the probability P(X < 4) when n = 36 1.721018e-2X
Transcribed Image Text:Suppose X is a Normal random variable with with expected value 5 and standard deviation 5. 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< 4.0) 0.03593032 X b) Find the probability P(X < 4) when n = 9 3.332045e-0X c) Find the probability P(X < 4) when n = 36 1.721018e-2X
> mu <- 5
> sigma <- 5
> pnorm(-4,mu ,sigma)
[1] 0.03593032
> pnorm(-4,mu,sigma/sqrt(9))
[1] 3.332045e-08
> pnorm(-4, mu, sigma/sqrt(36))
[1] 1.721018e-27
Transcribed Image Text:> mu <- 5 > sigma <- 5 > pnorm(-4,mu ,sigma) [1] 0.03593032 > pnorm(-4,mu,sigma/sqrt(9)) [1] 3.332045e-08 > pnorm(-4, mu, sigma/sqrt(36)) [1] 1.721018e-27
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