Since Jack’s head has a circumference in the 16th percentile, his head circumference is 56.0 centimeters.
What is percentile?
We know that In a normal distribution, a percentile is a value that has a certain percentage of observations below it.
The Z score is defined as "a numerical measurement used in statistics to determine a value's relationship to the mean (average) of a group of values, expressed in standard deviations from the mean."
Z score can be calculated as
Z = (x - μ)/σ
How to solve it?
Here, mean = μ = 57.5 centimeters
standard deviation = σ = 1.5 centimeters
Let the circumference of Jack’s head = x centimeters
The percentile = 16
Z value for 16 percentile = - 0.994
So, (x - 57.5)/1.5 = - 0.994
i.e. x - 57.5 = - 0.994*1.5 = - 1.491
i.e. x = - 1.491 + 57.5 = 56.009
The nearest tenth value for 56.009 is 56.0
Then Jack's head circumference is 56.0 centimeters.
Learn more about percentile here -
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