Answer to Question #326448 in Statistics and Probability for jaja

Question

A random variable X is normally distributed with a mean of 45 and standard deviation of 3. What is the value of the random variable X if the area to the left of Z is 0.1255

Answer 1

We look for 0.1255 inside the z-table.

Although 0.1255 does not appear, both 0.1251 and 0.1271 do, corresponding to z = -1.15 and -1.14, respectively.

Since 0.1255 is approximately one fifth way between the two probabilities that do appear, we assume Z = - 1.148.

So,

$Z=\cfrac{X-\mu}{\sigma};\\ X=Z\sigma+\mu=\\=-1.148\cdot3+45=41.556.$