Question
with a mean of 75 and a standard deviation of 10 what percentage is less than 85
Answers
GPT 3.5
To determine the percentage of values that are less than 85, we need to calculate the z-score for 85 first. The z-score formula is given by:
z = (x - μ) / σ
where:
x = value
μ = mean
σ = standard deviation
Plugging in the given values:
z = (85 - 75) / 10
z = 10 / 10
z = 1
Now, we need to find the cumulative probability associated with a z-score of 1. We can refer to the z-table or use a calculator to find this probability.
Using the z-table, the cumulative probability for a z-score of 1 is 0.8413. This means that approximately 84.13% of the values are less than 85.
Therefore, the percentage of values less than 85 is approximately 84.13%.
z = (x - μ) / σ
where:
x = value
μ = mean
σ = standard deviation
Plugging in the given values:
z = (85 - 75) / 10
z = 10 / 10
z = 1
Now, we need to find the cumulative probability associated with a z-score of 1. We can refer to the z-table or use a calculator to find this probability.
Using the z-table, the cumulative probability for a z-score of 1 is 0.8413. This means that approximately 84.13% of the values are less than 85.
Therefore, the percentage of values less than 85 is approximately 84.13%.