A population of values has a distribution with μ=211.8μ=211.8
and σ=33.1σ=33.1. You intend to draw a random sample of size
According to the Central Limit Theorem:
(a) What is the mean of the distribution of sample means?
(b) What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
(c) In a random sample of n=120, what is the probability that its random sample mean is more than 211? Round to three decimal places.
(d) In a random sample of n=120, what is the probability that its random sample mean is less than 214.2? Give your answer to three decimal places.
mean = = 211.8
standard deviation = = 33.1
n = 120
a) = = 211.8
b) = / n = 33.1 / 120 = 3.02
c) P( > 211) = 1 - P( < 211)
= 1 - P[( - ) / < (211 - 211.8) / 3.02 ]
= 1 - P(z < -0.26)
= 1 - 0.397
d) P( < 214.2) = P(( - ) / < (214.2 - 211.8) / 3.02)
= P(z < 0.79)
Using z table
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