To find the probability of a pulse rate between 65 beats per minute and 75 beats per minute, we need to calculate the area under the normal distribution curve between these two values.
First, let's calculate the z-scores for both 65 and 75 beats per minute using the formula:
z = (x - μ) / σ
Where:
- x is the value we want to find the z-score for (65 or 75 beats per minute),
- μ is the mean of the distribution (79.0 beats per minute),
- σ is the standard deviation of the distribution (12.5 beats per minute).
For 65 beats per minute:
z = (65 - 79.0) / 12.5 = -1.12
For 75 beats per minute:
z = (75 - 79.0) / 12.5 = -0.32
Now, we need to find the area under the curve between these two z-scores using a standard normal distribution table or a calculator.
Using the standard normal distribution table or a calculator, we find that the area to the left of -1.12 is approximately 0.1314 and the area to the left of -0.32 is approximately 0.3745.
To find the probability of a pulse rate between 65 and 75 beats per minute, we subtract the smaller area from the larger area:
Probability = 0.3745 - 0.1314 = 0.2431
Therefore, the probability of a pulse rate between 65 and 75 beats per minute is approximately 0.2431.