Question

The average heart rate is 72 beats per minute. Suppose the variable is approximately normal with a standard deviation of 3. Find the probability that a randomly selected person has a heart rate between 68 and 74 beats per minute.

Answer 1

To find the probability that a randomly selected person has a heart rate between 68 and 74 beats per minute, calculate the z-scores for both values and find the area under the standard normal distribution curve.

Step-by-step explanation:

To find the probability that a randomly selected person has a heart rate between 68 and 74 beats per minute, we need to calculate the z-scores for both values and then find the area under the standard normal distribution curve between those z-scores.

First, calculate the z-score for 68 beats per minute:

z = (68 - 72) / 3 = -4 / 3 ≈ -1.33

Next, calculate the z-score for 74 beats per minute:

z = (74 - 72) / 3 = 2 / 3 ≈ 0.67

Using a standard normal distribution table or a calculator, find the area under the curve between -1.33 and 0.67. This represents the probability that a randomly selected person has a heart rate between 68 and 74 beats per minute.