Final answer:
To find the probability that the mean pulse rate of 25 randomly selected adult females is between 69 and 81 beats per minute, calculate the z-scores for these values using the z-score formula. Then use a standard normal distribution table or calculator to find the probabilities associated with these z-scores. The probability is approximately 1, indicating a high likelihood.
Step-by-step explanation:
To find the probability that the mean pulse rate of 25 randomly selected adult females is between 69 beats per minute and 81 beats per minute, we need to calculate the z-scores for these two values. A z-score represents how many standard deviations a value is from the mean. We can use the z-score formula: z = (x - μ) / (σ / √n), where x is the value, μ is the mean, σ is the standard deviation, and n is the sample size.
First, we need to find the mean and standard deviation of the pulse rates. Let's assume that the mean is μ = 75 beats per minute and the standard deviation is σ = 5 beats per minute. Using the z-score formula, we can calculate the z-scores for 69 and 81 beats per minute:
z₁ = (69 - 75) / (5 / √25)
= -6 / 1
= -6
z₂ = (81 - 75) / (5 / √25)
= 6 / 1
= 6
Now, we can use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability of a z-score being less than -6 or greater than 6 is extremely low, since these values are significantly beyond the standard deviations.
Therefore, the probability that the mean pulse rate of 25 randomly selected adult females is between 69 beats per minute and 81 beats per minute is approximately 1.