Assume that females have pulse rates that are normally distributed with a mean of u =74.0 beats per minute and a standard deviation of o = 12,5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 81 beats per minute. The probability is (Round to four decimal places as needed.)
Assume that females have pulse rates that are normally distributed with a mean of u =74.0 beats per minute and a standard deviation of o = 12,5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 81 beats per minute. The probability is (Round to four decimal places as needed.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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6.4-1
![**Problem: Probability of Pulse Rates**
Assume that females have pulse rates that are normally distributed with a mean of \( \mu = 74.0 \) beats per minute and a standard deviation of \( \sigma = 12.5 \) beats per minute. Complete parts (a) through (c) below.
**a.** If 1 adult female is randomly selected, find the probability that her pulse rate is less than 81 beats per minute.
The probability is [_____]
(Round to four decimal places as needed.)
**Explanation:**
This problem involves calculating the probability under a Normal distribution. You are given the mean and standard deviation and are asked to find the probability for a specific range, which can be solved using the standard normal distribution (Z-score).
1. **Calculate the Z-score:**
The Z-score formula is:
\[ Z = \frac{X - \mu}{\sigma} \]
where \( X \) is the value we are finding the probability for, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
2. **Use the Z-score to find the probability:**
Once the Z-score is calculated, you can use a standard normal distribution table or calculator to find the probability that corresponds to that Z-score.
This type of problem is common in statistics to understand how data points relate to a normal distribution curve.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F12d9946b-1c78-40d9-ae41-75de22b19971%2F7e50ea7b-f932-4ae6-aa49-979987ab1616%2Fjjflb0p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Probability of Pulse Rates**
Assume that females have pulse rates that are normally distributed with a mean of \( \mu = 74.0 \) beats per minute and a standard deviation of \( \sigma = 12.5 \) beats per minute. Complete parts (a) through (c) below.
**a.** If 1 adult female is randomly selected, find the probability that her pulse rate is less than 81 beats per minute.
The probability is [_____]
(Round to four decimal places as needed.)
**Explanation:**
This problem involves calculating the probability under a Normal distribution. You are given the mean and standard deviation and are asked to find the probability for a specific range, which can be solved using the standard normal distribution (Z-score).
1. **Calculate the Z-score:**
The Z-score formula is:
\[ Z = \frac{X - \mu}{\sigma} \]
where \( X \) is the value we are finding the probability for, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.
2. **Use the Z-score to find the probability:**
Once the Z-score is calculated, you can use a standard normal distribution table or calculator to find the probability that corresponds to that Z-score.
This type of problem is common in statistics to understand how data points relate to a normal distribution curve.
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