Question
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?
Answers
GPT 3.5
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.
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.