A population of values has a normal distribution with \mu = 181 and \sigma = 41.8. You intend to draw a

Khaleesi Herbert 2021-02-05 Answered

A population of values has a normal distribution with μ=181 and σ=41.8. You intend to draw a random sample of size n=144.
Find the probability that a single randomly selected value is between 176.5 and 183.1.
P(176.5<M<183.1)=?
Write your answers as numbers accurate to 4 decimal places.

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Expert Answer

Tasneem Almond
Answered 2021-02-06 Author has 91 answers

Given that,
μ=181,
σ=41.8
n=144
The probability that a sample size, n=144 is randomly selected with a mean between 176.5 and 183.1 is,
P(176.5<X<183.1)=P(176.518141.8144<Xμσ144<183.118141.8144)
=P(1.292<z<0.603)
=P(z<0.603)P(z<1.292)
={(=NORMDIST(0.050))(=NORMDIST(0.108))}((Using Excelfunction,(=NORMDIST(z)))
=0.72670.0982=0.6285
Therefore, the required probability is, 0.6285.

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Jeffrey Jordon
Answered 2021-11-17 Author has 2064 answers

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