How to find probability density function

Question

I can't figure out how to solve for What is the probability of obtaining a standardized score less than or equal to 1.0 standard deviations from the mean? 

 

P (z ≤ 1.0) =  

Do I need to find the Z score first or at all? What do I use for X in my probability density function formula?

Mean= 94.94

SD=10.16

Answer 1

In the absence of indication to the contrary, I'll assume normal distribution.

Let's compute the probability of obtaining a score greater than 1 std deviation from the mean, then subtract that from 1 to get the final answer.

From a table, P(X > mean + 1 * std deviation) = P(X > 94.94 + 10.16) ≈ .1587

The normal distribution is symmetric, so P(X < mean - 1 * std deviation) is also .1587

Writing µ for mean and σ for std deviation,

P(|X - µ| ≤ σ) = 1 - [P(X < µ - σ) + P(X > µ + σ)] ≈ 1 - 2 * .1587 = .6826