# A population of values has a normal distribution with \mu = 216.9 and \sigma = 87.1. You intend to draw a random sample of size n = 97.Find the probability that a single randomly selected value is between 193 and 244.3.P(193<X<244.3) =?Write your answers as numbers accurate to 4 decimal places.

A population of values has a normal distribution with $\mu =216.9$ and $\sigma =87.1$. You intend to draw a random sample of size $n=97$.
Find the probability that a single randomly selected value is between 193 and 244.3.
$P\left(193?

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Theodore Schwartz

Step 1
From the provided information,
Mean $\left(\mu \right)=216.9$
Population standard deviation $\left(\sigma \right)=87.1$
Sample size $\left(n\right)=97$
$X\sim N\left(216.9,87.1\right)$
Step 2
The required probability that a single randomly selected value is between 193 and 244.3 can be obtained as:
$P\left(193
$=P\left(-0.274
$=P\left(Z<0.315\right)-P\left(Z<-0.274\right)$
$=0.6236-0.3920=0.2316$ (Using standard normal table)
Thus, the required probability is 0.2316.

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