Converting Percentiles to Statistics
A baby is born and his weight is in the \(15th\) percentile. What does this mean?
Often times, we are given a percentile or a probability that an event will occur, but we do not know the data value associated with it. We can look up the given area/probability in the body of our z-table to find the z-score, then solve for the data value x using the formula \(\large{z=\frac{x-\mu}{\sigma}}\).
Converting Percentages Back into Statistics:
1. Draw the Standard Normal Distribution and place the given percentage in the curve in the appropriate location.
2. Using the table, determine the z-score that corresponds to the area from \(0\) to the boundary line.
3. Replace the z-score value, the mean, and the standard deviation into the z-score formula to solve for \(x\).
4. Write your answer in context.
Example 1: The weights of newborn babies vary normally with a mean of \(7.5\) pounds and a standard deviation of \(1.25\) pounds. Philip was in the \(15th\) percentile when he was born. How much did he weigh?
A baby is born and his weight is in the \(15th\) percentile. What does this mean?
- It means that this baby weighs more than just \(15\%\) of newborns.
Often times, we are given a percentile or a probability that an event will occur, but we do not know the data value associated with it. We can look up the given area/probability in the body of our z-table to find the z-score, then solve for the data value x using the formula \(\large{z=\frac{x-\mu}{\sigma}}\).
Converting Percentages Back into Statistics:
1. Draw the Standard Normal Distribution and place the given percentage in the curve in the appropriate location.
2. Using the table, determine the z-score that corresponds to the area from \(0\) to the boundary line.
3. Replace the z-score value, the mean, and the standard deviation into the z-score formula to solve for \(x\).
4. Write your answer in context.
Example 1: The weights of newborn babies vary normally with a mean of \(7.5\) pounds and a standard deviation of \(1.25\) pounds. Philip was in the \(15th\) percentile when he was born. How much did he weigh?
You can also find the z-score using the graphing calculator. Take a look at the flowchart below, then watch the video to see Example 1 completed with the calculator.
Area represents the area of the left tail, which is the area from negative infinity to the boundary line.
Example 2: The lengths of newborn babies vary normally with a mean of \(120\) inches and standard deviation of \(1.2\) inches. The middle \(58\%\) of newborn babies are between what lengths?