Assuming the resting heart rates for a sample of individuals are normal distibuted with a mean of 70 and a standard deviation of 15. Waht percentage of rates less than 70
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to your Z score. Change to percentage.
4.62
To find the percentage of heart rates that are less than 70, we need to calculate the area under the normal distribution curve to the left of 70.
Here's how you can do it step by step:
Step 1: Sketch the normal distribution curve.
Draw a bell-shaped curve with the center at the mean, which is 70 in this case. The standard deviation is 15, so on your curve, one standard deviation below the mean would be at 55, and two standard deviations below the mean would be at 40.
Step 2: Calculate the Z-score.
The Z-score is a measure of how many standard deviations a particular value is from the mean. To find the Z-score for 70, we can use the formula:
Z = (X - μ) / σ
Where:
X is the value we're interested in (70 in this case),
μ is the mean (70), and
σ is the standard deviation (15).
Substituting the values into the formula, we get:
Z = (70 - 70) / 15 = 0
Step 3: Look up the Z-score in the standard normal distribution table.
The standard normal distribution table provides the area under the curve to the left of a given Z-score. In our case, since the Z-score is 0, the corresponding area in the table is 0.5000.
Step 4: Calculate the percentage.
Since the Z-score of 0 corresponds to an area of 0.5000 in the standard normal distribution table, we can say that 50% of the heart rates are less than 70.
Therefore, the percentage of heart rates that are less than 70 is 50%.