A population of values has a normal distribution with \mu = 133.5 and \sigma = 5.2. You intend

he298c 2021-02-05 Answered

A population of values has a normal distribution with μ=133.5 and σ=5.2. You intend to draw a random sample of size n=230.
Find the probability that a sample of size n=230 is randomly selected with a mean between 133.6 and 134.1.
P(133.6<x<134.1)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

delilnaT
Answered 2021-02-06 Author has 94 answers

Given Information:
μ=133.5 and σ=5.2
n=230
To find the probability that a sample of size n=230 is randomly selected with a mean between 133.6 and 134.1:
Based on the concept of Central limit theorem, if a random sample of size 'n' is drawn from a population with mean μ and standard deviation σ, the sampling distribution of sample mean x is approximately normally distributed with mean μx=μ and standard deviation σx=σn.
Mean of sample mean = μx=μ=133.5
Standard deviation σx=σn=5.2230=0.343
Required probability can be obtained as follows:
P(133.6<x<134.1)=P(x<134.1)P(x<133.6)
=P(xμσ<134.1133.50.343)P(xμσ<133.6133.50.343)
=P(Z<1.75)P(Z<0.29)
=0.959940.61409=0.34585[using standard altab]
Therefore, probability that a sample of size n=230 is randomly selected with a mean between 133.6 and 134.1 is 0.3459

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Jeffrey Jordon
Answered 2021-11-14 Author has 2070 answers

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