Final answer:
The probability of a pulse rate between 61 and 73 beats per minute is found by converting these values to their Z-scores and subtracting the probability of the lower Z-score from the probability of the higher Z-score.
Step-by-step explanation:
To find the probability of a pulse rate between 61 beats per minute and 73 beats per minute for an adult female, given that the pulse rates are normally distributed with a mean (μ) of 77.0 beats per minute and a standard deviation (σ) of 12.5 beats per minute, we need to use the standard normal distribution (the Z-distribution).
First, we convert the pulse rates of 61 and 73 beats per minute to their corresponding Z-scores using the formula:
Z = (X - μ) / σ
For 61 beats
Z1 = (61 - 77.0) / 12.5 = -1.28
For 73 beats:
Z2 = (73 - 77.0) / 12.5 = -0.32
Then, we look up these Z-scores in the standard normal distribution table or use a normal distribution calculator to find the probabilities corresponding to Z1 and Z2.
Finally, we subtract the probability corresponding to Z1 from the probability corresponding to Z2 to find the desired probability.