Suppose x is a Normal random variable with with expected value 7 and standard de
ID: 2936216 • Letter: S
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