Suppose x is a Normal random variable with with expected value 7 and standard de

Question

Suppose x is a Normal random variable with with expected value 7 and standard deviation 0.42. 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>7.2)

b) Find the probability P(x)>7.2 when n = 9

c) Find the probability P(x)>7.2 when n = 25

d) What is the probability P(6.9 <x<7.2) when n = 16?

e) What is the standard deviation of x when n = 25

f) What is the probability that

X1 + X2 + ... +X25 < 176

Explanation / Answer

a) > 1 - pnorm(7.2, 7, 0.42)
[1] 0.3169693

b) > 1 - pnorm(7.2, 7, 0.42/sqrt(9))
[1] 0.07656373

c) > 1 - pnorm(7.2, 7, 0.42/sqrt(25))
[1] 0.008633972

d)> pnorm(7.2, 7, 0.42/sqrt(16)) - pnorm(6.9, 7, 0.42/sqrt(16))
[1] 0.8011426

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