# A distribution of values is normal with a mean of 166.1 and a standard deviation of 73.5.Find the probability that a randomly selected value is between 151.4 and 283.7.P(151.4 < X < 283.7) = IncorrectWrite your answers as numbers accurate to 4 decimal places.

A distribution of values is normal with a mean of 166.1 and a standard deviation of 73.5.
Find the probability that a randomly selected value is between 151.4 and 283.7.
$P\left(151.4 Incorrect

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Step 1
Solution:
Let X be the value.
From the given information, X follows normal distribution with a mean $\mu =166.1$ and a standard deviation is $\sigma =73.5$.
Step 2
Then, the probability that a randomly selected value is between 151.4 and 283.7 is
$P\left(151.4
$=P\left(-0.200
$=P\left(Z<1.600\right)-P\left(Z<-0.200\right)$
$=0.9452-0.4207\left[\begin{array}{c}\text{Using the excel function}\\ =\text{NORM.DIST}\left(1.600,0,1,TRUE\right)\\ =\text{NORM.DIST}\left(-0.200,0,1,TRUE\right)\end{array}\right]\phantom{\rule{0ex}{0ex}}=0.5245$
Thus, the probability that a randomly selected value is between 151.4 and 283.7 is 0.5245.

Jeffrey Jordon