Question

Given a normally distributed variable X with mean 18 and standard deviation 2.5, find;

P(X < 15)

Answer 1

P(X < 15) for a normally distributed variable with mean 18 and standard deviation 2.5, calculate the Z-score for X = 15, then use the standard normal distribution table or a calculator to find that probability.

Step-by-step explanation:

To find the probability P(X < 15) for a normally distributed variable X with a mean (μ) of 18 and a standard deviation (σ) of 2.5, you can use the standard normal distribution or Z-score formula.

First, we calculate the Z-score for X = 15 using the formula:

Z = (X - μ) / σ

Z = (15 - 18) / 2.5

Z = -1.2

Now, look up the Z-score of -1.2 on the standard normal distribution table, or use a calculator's normal distribution function, to find P(Z < -1.2).


This gives you the same probability as P(X < 15) since the standard normal distribution is just a special case of the normal distribution with a mean of 0 and a standard deviation of 1.

The value from the standard normal distribution table or calculator would provide the desired probability.