The scores on a psychology exam were normally distributed with a mean of 56 and a standard deviation of 6. About what percentage of scores were less than 50?
To find the percentage of scores that were less than 50, we need to calculate the z-score of 50, which measures how many standard deviations below the mean 50 is.
The formula for calculating the z-score is:
z = (x - μ) / σ
where:
x = the value we want to find the z-score for (50 in this case)
μ = the mean (56)
σ = the standard deviation (6)
Plugging in the values, we get:
z = (50 - 56) / 6
z = -6 / 6
z = -1
Now, we need to find the percentage of scores that have a z-score less than -1. We can use a standard normal distribution table or a calculator to find this probability.
According to the standard normal distribution table, the area to the left of z = -1 is approximately 0.1587. This means that approximately 15.87% of scores were less than 50.
So, about 15.87% of scores were less than 50.