To find the proportion of men who have a pulse rate greater than 78, we can use the concept of the standard normal distribution. Here's how you can do it:
Convert the given pulse rate of 78 beats per minute to a standard score (also known as a z-score). The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
x is the value we want to convert to a z-score (in this case, 78)
μ is the mean of the distribution (70)
σ is the standard deviation of the distribution (8)
Plugging in the values, we get:
z = (78 - 70) / 8 = 8 / 8 = 1
So, the z-score for a pulse rate of 78 is 1.
Once we have the z-score, we can find the proportion of men with a pulse rate greater than 78 by looking up the area to the right of the z-score on a standard normal distribution table or using statistical software.
The area to the right of a z-score of 1 represents the proportion of values greater than that z-score. So, we need to find the area to the right of z = 1.
By referring to a standard normal distribution table or using statistical software, we can find that the area to the right of z = 1 is approximately 0.1587.
Therefore, the proportion of men who have a pulse rate greater than 78 is approximately 0.1587 or 15.87%.
I hope this helps you further explore the topic of finding the proportion of men with a pulse rate greater than 78. Let me know if you have any more questions!