Assume that the random variable X is normally distributed with mean μ = 120 and standard deviation σ = 13. Find P(X <105).

To find P(X < 105), we first need to convert the raw score of X = 105 to a z-score. The z-score is a measure of how many standard deviations an element is from the mean.

The formula to calculate the z-score is:

Z = (X - μ) / σ

where: X = raw score μ = mean σ = standard deviation

Substituting the given values into the formula, we get:

Z = (105 - 120) / 13 = -1.15

Now, we need to find the probability that Z is less than -1.15. We can find this by looking up -1.15 in the standard normal distribution table, or using a calculator or software that can calculate it.

The standard normal distribution table shows that the probability for Z < -1.15 is approximately 0.1251.

So, P(X < 105) = P(Z < -1.15) = 0.1251 or 12.51%.