A population of values has a normal distribution with \mu=192.6 and \sigma=34.4.

defazajx 2021-02-25 Answered

A population of values has a normal distribution with μ=192.6 and σ=34.4. You intend to draw a random sample of size n=173.
Find the probability that a sample of size n=173 is randomly selected with a mean less than 186.1.
P(M<186.1)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

irwchh
Answered 2021-02-26 Author has 102 answers

Step 1
Given:
μ=192.6,
σ=34.4,
n=173.
The Z-score follows standard normal distribution.
Step 2
P[X<186.1]=P[Xμσn<186.1192.634.4173]
=P[Z<2.49]=0.0066 (Use standard normal table)
The probability that a sample of size n=173 is randomly selected with a mean less than 186.1 is 0.0066.

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