Solution:
A)Given that,
μ =202.5 cm , σ=7.8 cm
a)
P(X>211.80)=1-P(X<=211.80)
=1- p{[(x- μ)/σ]<=[(211.80- 202.5)/7.8]}
= 1- P(z<=1.19 )
=1-0.8830 ( From Standard Normal table)
=0.1170
The required probability is 0.1170
b)
Given that,
n=15
By using the definition of central limit theorem,
For a random sample of size n , sample mean is equal to the
population mean
i.e. μx̄ = μ and
sample standard deviation can be calculated as
σx̄=σ/(√n)
Therefore,
μx̄ = μ= 202.5
And
σx̄=σ/(√n)
= 7.8/(√15)
= 2.0140
A)
P(x̄>201.00)= 1 - P(x̄<=201.00)
= 1- P{[ (x̄-μx̄ ) /σx̄]<=[(201.00 - 202.5)/2.0140]}
=1- P (Z < -0.74) ( From. Standard Normal table)
= 1- 0.2296
= 0.7704
The required probability is 0.7704
C)
Correct answer: A
The normal distribution can be used because the original population
has a normal distribution.
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