A population of values has a normal distribution with \mu=116.3 and \sigma=27.5. You intend to draw a random sample of size n=249. Find the probabilit

Lewis Harvey

Lewis Harvey

Answered question

2021-02-11

A population of values has a normal distribution with μ=116.3 and σ=27.5. You intend to draw a random sample of size n=249.
Find the probability that a sample of size n=249 is a randomly selected with a mean greater than 117.3.
P(X>117.3)=?
Write your answers as numbers accurate to 4 decimal places.

Answer & Explanation

Aamina Herring

Aamina Herring

Skilled2021-02-12Added 85 answers

X=1ni=1nXi=
Mean value.
Therefore, the mean of X is 116.3,
standard deviation is 27.5n=27.5249, as n=249.
The probability of a mean greater than 117.3 is
P[X>117.3]
=P[X116.327.5249>117.3116.327.5249]
=P[Z>24927.5],Z=X116.327.5249 Normal(0,1)
=1P[Z24927.5]
=1ϕ(0.574)
=10.717=0.283
The value of ϕ(0.574) is taken from the Normal distribution table.
Therefore, the probability of the mean is greater than 117.3 is 0.283.

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?