defazajx

2020-10-26

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\left(184?
Write your answers as numbers accurate to 4 decimal places.

### Answer & Explanation

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
$=P\left(-0.214
$=P\left(z<0.091\right)-P\left(z<-0.214\right)$
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
$=0.5363-0.4153=0.1210$
Thus, the probability that a single randomly selected value is between 184 and 205.1 is 0.1210.

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