Question

The mean pulse rate for adults is 72 beats per minute (www.healthepic.com) and let’s suppose that the standard deviation is 11 bpm. Find: a. The probability that a randomly chosen adult has a pulse rate over 77 bpm assuming that the rates are normally distributed. b. The probability that a random sample of 19 adults will have a mean beats per minute over 77.

Answer 1

To find the probability of an adult having a pulse rate over 77 bpm, calculate the Z-score and refer to a Z-table or normal distribution calculator. Similarly, for the probability of a sample mean of 19 adults exceeding 77 bpm, calculate the Z-score using the standard error of the mean and consult the Z-table.

Step-by-step explanation:

Finding Probability in a Normal Distribution

To solve these problems, we will apply principles of the normal distribution using the provided mean and standard deviation.

a. Probability of an Adult Having a Pulse Rate Over 77 bpm:

The Z-score is calculated as follows:

Z = (X - μ) / σ

Where X is the value of interest (77 bpm), μ is the mean (72 bpm), and σ is the standard deviation (11 bpm).

Z = (77 - 72) / 11 = 0.4545

Using a Z-table or normal distribution calculator, we find the probability of a Z-score being above 0.4545. This value is equivalent to 1 minus the probability of Z being less than 0.4545.

b. Probability of a Random Sample of 19 Adults Having a Mean Over 77 bpm:

When considering a sample, we use the standard error of the mean (SEM), which is σ/√n, where n is the sample size.

SEM = 11 / √19 = 2.525

We calculate the Z-score using the SEM:

Z = (77 - 72) / 2.525 = 1.9802

Again, we'd look up the probability associated with this Z-score to find the probability of the mean of a sample of 19 adults being over 77 bpm.