Solved:
Answered by AI, Verified by Human Experts
A variable is normally distributed with a mean of 16 and a standard deviation of 6. Find the percent of the data set:
A variable is normally distributed with a mean of 16 and a standard deviation of 6. Find the percent of the data set:
Final answer:To find thepercent of the data set, you can calculate the z-score using the formula z = (x - μ) / σ, where x is the value you want to find the percentile for, μ is the mean, and σ is the standard deviation.Then, you can reference the standard normal distribution table or use a calculator to find the corresponding percentage.For example, if you want to find the percent of data below 20, the z-score is 0.67 and thecorresponding percentage is approximately 74.86%.Explanation:To find thepercent of the data set, we need to determine the range of values within a certain percentage.In this case, we can use the standard normal distribution table or a calculator to find the z-score corresponding to the desired percentile.With the given mean of 16 and standard deviation of 6, we can calculate the z-score using the formula z = (x - μ) / σ, where x is the value we want to find the percentile for, μ is the mean, and σ is the standard deviation.For example, if we want to find the percent of data below 20, we first calculate the z-score: z = (20 - 16) / 6 = 0.67.Referencing the standard normal distribution table or using a calculator, we find that the area to the left of a z-score of 0.67 is approximately 0.7486 or 74.86%.Therefore, approximately74.86% of the data set is below 20.Learn more about Calculating Percentiles in a Normal Distribution here:brainly.com/question/33620294#SPJ1...