defazajx

2020-10-26

A population of values has a normal distribution with

Find the probability that a single randomly selected value is between 184 and 205.1.

Write your answers as numbers accurate to 4 decimal places.

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,

$P\left(184<X<205.1\right)=P\left(\frac{184-198.8}{69.2}<\frac{X-\mu}{\sigma}<\frac{205.1-198.8}{69.2}\right)$

$=P\left(-0.214<z<0.091\right)$

$=P\left(z<0.091\right)-P\left(z<-0.214\right)$

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,

$P\left(184<X<205.1\right)=P\left(z<0.091\right)-P\left(z<-0.214\right)$

$=0.5363-0.4153=0.1210$

Thus, the probability that a single randomly selected value is between 184 and 205.1 is 0.1210.

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