A population of values has a normal distribution with \mu=154.5 and \sigma=96.1. You intend to draw a random sample of size n=134. Find the probabilit

CheemnCatelvew 2020-11-09 Answered
A population of values has a normal distribution with μ=154.5 and σ=96.1. You intend to draw a random sample of size n=134.
Find the probability that a sample of size n=134 is randomly selected with a mean greater than 167.
P(M>167)=?
Write your answers as numbers accurate to 4 decimal places.
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Expert Answer

Macsen Nixon
Answered 2020-11-10 Author has 117 answers
X1,X2,X134 be a random sample from Normal distribution with μ=154.5 and σ=96.1.
Then the sample mean
M=1134i=1134Xi follows Normal distribution with mean 154.5 and standard deviation 96.1134.
Hence, the probability that sample mean greater than 167.
P(M>167)
=1P(M167)
=1P(M154.596.1134167154.596.1134)
=1P(Z1.506),Z=(M154.596.1134) follows Normal (0,1)
=1ϕ(1.506),ϕ(1.506) calculated from Normal distribution table.
=10.934=0.066
Therefore, the probability that a sample of size n=134 is randomly selected with a mean greater than 167 is 0.066.
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