If μ = 500 and σ =10, z = -3.0 falls how many points below the mean?
To determine how many points below the mean a particular value falls, we can use the standard normal distribution and the concept of z-scores.
A z-score represents the number of standard deviations a given value is from the mean. It tells us the position of a value in a distribution relative to the mean.
In this case, we are given that the mean (μ) is 500 and the standard deviation (σ) is 10. We are also given that the z-score is -3.0.
To calculate how many points below the mean a z-score of -3.0 falls, we look at the standard normal distribution table or use a calculator.
The standard normal distribution table provides the cumulative probability associated with each z-score. This cumulative probability represents the area under the curve to the left of a given z-score.
A z-score of -3.0 falls to the left of the mean and represents a very low value in the distribution. Using a standard normal distribution table or calculator, we find that the cumulative probability associated with a z-score of -3.0 is approximately 0.0013.
This means that only 0.13% of the values in the distribution fall below the given value. Therefore, a z-score of -3.0 falls approximately in the bottom 0.13% of the distribution, which corresponds to the number of points below the mean.
In terms of the given values, it means that the value associated with this z-score falls approximately 0.13% below the mean.