Question

# A population of values has a distribution with μ=211.8μ=211.8 and σ=33.1σ=33.1. You intend to draw a...

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 n=120n=120.

According to the Central Limit Theorem:

(a) What is the mean of the distribution of sample means?
μ¯x=μx¯=

(b) What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
σ¯x=σx¯=

(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.

Solution :

Given that,

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

= 0.603

d) P( < 214.2) = P(( - ) / < (214.2 - 211.8) / 3.02)

= P(z < 0.79)

Using z table

= 0.785

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