Assume that females have pulse rates that are normally distributed with a mean of beats per minute and a standard deviation of beats per minute. Complete parts (a) through © below.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute.
The probability is
(Round to four decimal places as needed.)

Ask by Reyes Grant. in the United States

Mar 20,2025

Question

Assume that females have pulse rates that are normally distributed with a mean of beats per minute and a standard deviation of beats per minute. Complete parts (a) through © below.
a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute.
The probability is
(Round to four decimal places as needed.)

Ask by Reyes Grant. in the United States

Mar 20,2025

UpStudy AI · Accepted Answer

1. The pulse rate $$X$$ is normally distributed with mean $$\mu = 72.0$$ beats per minute and standard deviation $$\sigma = 12.5$$ beats per minute.
2. To find the probability that a randomly selected adult female has a pulse rate less than 78 beats per minute, we standardize the variable:
   $$
   z = \frac{X - \mu}{\sigma} = \frac{78 - 72}{12.5} = \frac{6}{12.5} = 0.48.
   $$
3. Using the standard normal distribution, the probability is:
   $$
   P(X < 78) = P(Z < 0.48).
   $$
4. From the standard normal table (or a calculator), we find:
   $$
   P(Z < 0.48) \approx 0.6844.
   $$

Thus, the probability that an adult female has a pulse rate less than 78 beats per minute is $$\boxed{0.6844}$$.
The probability that an adult female has a pulse rate less than 78 beats per minute is 0.6844.

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