A population of values has a normal distribution with \mu = 192.3 and \sigma = 66.5. You intend to draw a random sample of size n = 15. Find the proba

Dolly Robinson 2020-10-27 Answered

A population of values has a normal distribution with μ=192.3 and σ=66.5. You intend to draw a random sample of size n=15.
Find the probability that a sample of size n=15 is randomly selected with a mean less than 185.4.
P(M<185.4)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Cristiano Sears
Answered 2020-10-28 Author has 96 answers

The known values are,
μ=192.3,
σ=66.5,
n=15
The probability that a sample size n=15 is randomly selected with a mean less than 185.4 is,
P(M<185.4)=P(Mμσn<185.4192.366.515)
=P(z<0.402)
=0.3438420.3438
Therefore, the required probability is, 0.3438

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