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

opatovaL

Answered question

2021-01-27

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.

Answer & Explanation

Luvottoq

Luvottoq

Skilled2021-01-28Added 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.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?