A population of values has a normal distribution with \mu=120.6 and \sigma=48.5. You intend to draw a random sample of size n=105. Find the probabilit

Efan Halliday 2020-10-25 Answered
A population of values has a normal distribution with μ=120.6 and σ=48.5. You intend to draw a random sample of size n=105.
Find the probability that a sample of size n=105 is randomly selected with a mean greater than 114.9.
P(M>114.9)=?
Write your answers as numbers accurate to 4 decimal places.
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Expert Answer

Asma Vang
Answered 2020-10-26 Author has 93 answers

Step 1
Solution:
Let X be the value.
From the given information, X follows normal distribution with mean μ=120.6 and a standard deviation σ=48.5. The sample size is 105.
Step 2
The probability that a sample of size n=105 is randomly selected with a mean greater than 114.9 is
P(M>114.9)=P(Mμσn>114.9120.648.5105)
=P(Z>105(5.7)48.5)
=P(Z1.204)
=1P(Z<1.204)
=10.1143=0.8857[Using the excel function=NORM.DIST(0.118,0,1,TRUE)]

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Jeffrey Jordon
Answered 2021-11-17 Author has 2070 answers
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