Let's start by drawing a normal distribution showing resting heart rate. We will also include the interval of heart rates that are considered to be the average for women Aurora's age. That is 70 to 79 beats per minute.
To determine the percentage that this part represents of the total population, we can use the normal distribution function on a graphing calculator. On the calculator push 2nd, then VARS, and pick the second option.
Now, we need to type the parameters of the distribution. Based on the chart, the lower limit is 70 and the upper limit is 79. We are also given that the mean of the distribution is μ = 74 and the standard deviation is σ = 5. Let's type these values into the calculator!
Having entered all of the values, push ENTER to get a result.
As we can see, about 63 % of Aurora's classmates should fall in the average range.
b
This time we want to find the percentage of people whose resting heart rate is less than or equal to 66. Let's mark the corresponding interval below.
Again, we can use the normal distribution function on the graphing calculator. In this case, the upper limit is 66. For the lower limit we will put some arbitrary very low number to make sure we cover nearly everything in the left tail of the normal distribution. Recall that μ= 74 and σ = 5.
About 5.5 % of the classmates are in excellent shape.
c
By lowering the mean by 4, we have a new normal distribution curve with the mean of 70. We assume that the standard deviation is still 5.
Again, let's pull out the graphing calculator and use the normal distribution function. We will type the same parameters as in Part B, except for the new mean, μ = 70.
About 21 % of the classmates are now in excellent shape. If we subtract the percentage points in Part B from this number, we can determine the increase in the proportion of women classified as in excellent shape.
21 % -5.5 % = 15.5 %
The increase in the proportion is by about 16 percentage points.
