A population of values has a normal distribution with \mu=116.3 and \sigma=27.5. You intend to draw a random sample of size n=249. Find the probabilit

Lewis Harvey 2021-02-11 Answered
A population of values has a normal distribution with μ=116.3 and σ=27.5. You intend to draw a random sample of size n=249.
Find the probability that a sample of size n=249 is a randomly selected with a mean greater than 117.3.
P(X>117.3)=?
Write your answers as numbers accurate to 4 decimal places.
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Expert Answer

Aamina Herring
Answered 2021-02-12 Author has 85 answers
X=1ni=1nXi=
Mean value.
Therefore, the mean of X is 116.3,
standard deviation is 27.5n=27.5249, as n=249.
The probability of a mean greater than 117.3 is
P[X>117.3]
=P[X116.327.5249>117.3116.327.5249]
=P[Z>24927.5],Z=X116.327.5249 Normal(0,1)
=1P[Z24927.5]
=1ϕ(0.574)
=10.717=0.283
The value of ϕ(0.574) is taken from the Normal distribution table.
Therefore, the probability of the mean is greater than 117.3 is 0.283.
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