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 probability that a single randomly selected value is greater than 167. P(X > 167) =? Write your answers as numbers accurate to 4 decimal places.

opatovaL 2021-01-27 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 single randomly selected value is greater than 167.
P(X>167)=?
Write your answers as numbers accurate to 4 decimal places.
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Expert Answer

Luvottoq
Answered 2021-01-28 Author has 95 answers
Step 1
A population of values has a normal distribution with μ=154.5 and σ=96.1.
Step 2
X be a sample from the Normal distribution with μ=154.5 and σ=96.1.
The probability that a single randomly selected value is greater than 167.
P(X>167)
=1P(X167)
=1P(X154.596.1167154.596.1)
=1P(Z0.13),asZ=(X154.596.1) follows Normal(0,1)
=1ϕ(0.13),ϕ(0.13) calculated from Normal distribution table.
=10.5517=0.4483
Therefore, the probability that a single randomly selected value is greater than 167 is 0.4483.
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