A population of values has a normal distribution with \mu=73.1 and \sigma=28.1. You intend to draw a random sample of size n=131. Find the probability

babeeb0oL 2021-02-08 Answered
A population of values has a normal distribution with μ=73.1 and σ=28.1. You intend to draw a random sample of size n=131.
Find the probability that a sample of size n=131 is randomly selected with a mean greater than 69.7.
P(M>69.7)=?
Write your answers as numbers accurate to 4 decimal places.
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Expert Answer

joshyoung05M
Answered 2021-02-09 Author has 97 answers
Step 1
Let us denote X= population values
Given that X follows a normal distribution with mean =μ=73.1 and standard deviation =σ=28.1
Step 2
n=sample size = 131
So, M=X follows a normal distribution with mean =μ=73.1 and standard deviation =σn=28.1131=2.45510839922
the probability that a sample of size n=131 is randomly selected with a mean greater than 69.7.
P(M>69.7)
=P(Z>69.773.12.45510839922)=0.9170
Answer: 0.9170
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