the mean on the SAT verbal test is 505 with a standard deviation of 111. Assume the variable is normally distributed. Find the probability that the test scores are less than 600
600 = 505+95 = µ + 0.856σ
So, you want to look up in your Z table for P(Z<.856)
To find the probability that the test scores are less than 600, we need to calculate the z-score and then refer to the standard normal distribution table.
First, we calculate the z-score using the formula:
z = (x - μ) / σ
Where:
x = 600 (the test score you want to find the probability for)
μ = 505 (mean)
σ = 111 (standard deviation)
Substituting the values:
z = (600 - 505) / 111
z = 0.855
Next, we refer to the standard normal distribution table or use a calculator to find the corresponding probability associated with the z-score 0.855.
Using the standard normal distribution table, we can find the value of the cumulative probability:
P(Z < 0.855) = 0.8023
So, there is a probability of approximately 0.8023 (or 80.23%) that the test scores are less than 600 on the SAT verbal test.