A population of values has a normal distribution with \mu=198.8 and \sigma=69.2. You intend to draw a random sample of size n=147.Find the probability that a single randomly selected value is between 184 and 205.1.P(184 < X < 205.1) =?Write your answers as numbers accurate to 4 decimal places.

defazajx

defazajx

Answered question

2020-10-26

A population of values has a normal distribution with μ=198.8 and σ=69.2. You intend to draw a random sample of size n=147.
Find the probability that a single randomly selected value is between 184 and 205.1.
P(184<X<205.1)=?
Write your answers as numbers accurate to 4 decimal places.

Answer & Explanation

komunidadO

komunidadO

Skilled2020-10-27Added 86 answers

The mean is 198.8, standard deviation is 69.2, and sample size is 147.
The probability that a single randomly selected value is between 184 and 205.1 is,
P184<X<205.1=P184-198.869.2<X-μσ<205.1-198.869.2
=P-0.214<z<0.091
=Pz<0.091-Pz<-0.214
The probability of z less than 0.091 can be obtained using the excel formula “=NORM.S.DIST(0.091,TRUE)”. The probability value is 0.5363.
The probability of z less than –0.214 can be obtained using the excel formula “=NORM.S.DIST(–0.214,TRUE)”. The probability value is 0.4153.
The required probability value is,
P184<X<205.1=Pz<0.091-Pz<-0.214
=0.53630.4153=0.1210
Thus, the probability that a single randomly selected value is between 184 and 205.1 is 0.1210.

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