# A population of values has a normal distribution with \mu = 133.5 and \sigma = 5.2. You intend to draw a random sample of size n = 230. Find the proba

A population of values has a normal distribution with $\mu =133.5$ and $\sigma =5.2$. You intend to draw a random sample of size $n=230$.
Find the probability that a single randomly selected value is between 133.6 and 134.1.
$P\left(133.6?

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Clelioo

Given Information:
$\mu =133.5$ and $\sigma =5.2$
$n=230$
To find the probability that a single randomly selected value is between 133.6 and 134.1:
z-score is a measure which tells how many standard deviations away a data value is from the mean and is given by the formula:
$z=\frac{X-\mu }{\sigma }$
Required probability can be obtained as follows:
$P\left(133.6
$=P\left(\frac{X-\mu }{\sigma }<\frac{134.1-133.5}{5.2}\right)-P\left(\frac{133.6-133.5}{5.2}\right)$
$=P\left(Z<0.12\right)-P\left(Z<0.02\right)$

Using a standard normal table, look up for z-score 0.12 i.e., 0.1 in the row and 0.02 along the column. The intersection of both values is 0.54776.
Similarly, probability corresponding to z-score 0.02 is 0.50798.
Then, subtract the lower probability value from the higher value.
Therefore, probability that a single randomly selected value is between 133.6 and 134.1 is 0.0398.

Jeffrey Jordon

Answer is given below (on video)