Question

Suppose a normal distribution has a mean of 50 and a standard deviation of3. What is P(x < 53)?

Answer 1

Normal Distribution

Given a normal distribution of known mean μ and standard deviation σ, the z-score for a given parameter x value is:

$z=\frac{x-\mu}{\sigma}$

Let's calculate the z-score for x = 53, μ = 50, and σ = 3:

$z=\frac{53-50}{3}=1$

To calculate the required probability, we use a digital o physical table where the value of the z-score is used as a parameter.

The table gives us the 'left-tail" area of the bell curve, meaning the values of z are less or equal to that specific value.

Using an online table (or Excel, etc), we find:

P(z<1) = 0.8413

Or, equivalently,

P(x<53) = 0.8413