A population of values has a normal distribution with \mu=239.5 and \sigma=32.7.

Globokim8

Globokim8

Answered question

2020-10-25

A population of values has a normal distribution with μ=239.5 and σ=32.7. You intend to draw a random sample of size n=139.
Find the probability that a sample of size n=139 is randomly selected with a mean greater than 235.9.
P(M>235.9)=?
Write your answers as numbers accurate to 4 decimal places.

Answer & Explanation

aprovard

aprovard

Skilled2020-10-26Added 94 answers

From the provided information,
Mean (μ)=239.5
Standard deviation (σ)=32.7
Sample size (n)=139
Let X be a random variable which represents the value score.
XN(239.5,32.7)
The required probability that a sample of size n=139 is randomly selected with a mean greater than 235.9 can be obtained as:
P(M>235.9)=P(Mμσn>235.9239.532.7139)
=P(Z1.298)
=1P(Z<1.298)
=10.0971=0.9029 (Using standard normal table)
Hence, the required probability is 0.9029.

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