### Normal Distribution of Female Pulse RatesThis educational section will guide you through solving problems related to the normal distribution of female pulse rates. Assumptions and detailed steps are provided to aid learning.#### Problem StatementAssume that females have pulse rates that are normally distributed with:- A mean ($\mu$) of 73.0 beats per minute.- A standard deviation ($\sigma$) of 12.5 beats per minute.Complete parts (a) through (c) given below:#### Part (a)**Question:**If one adult female is randomly selected, find the probability that her pulse rate is less than 76 beats per minute.**Solution:**1. Use the Z-score formula: \[ Z = \frac{X - \mu}{\sigma} \] where $X$ is the value of interest (76 beats per minute).2. Calculate the Z-score: \[ Z = \frac{76 - 73.0}{12.5} \]3. Use the Z-score to find the corresponding probability from the standard normal distribution table or using statistical software.**The probability is $\square$** (Round to four decimal places as needed.)#### Part (b)**Question:**If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute. **Solution:**1. Use the distribution of the sample mean with the standard error ($\sigma_{\bar{X}}$): \[ \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} \] where $ n = 4 $.2. Calculate the standard error: \[ \sigma_{\bar{X}} = \frac{12.5}{\sqrt{4}} \]3. Use the Z-score formula for the sample mean: \[ Z = \frac{X_{\bar{X}} - \mu}{\sigma_{\bar{X}}} \] where $ X_{\bar{X}} $ is the sample mean of interest (76 beats per minute).4. Calculate the Z-score: \[ Z = \frac{76 - 73.0}{\frac{12.5}{2}} \]5. Use the Z-score to find the corresponding probability from the standard normal distribution table or using statistical software.**The

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Question Help v Assume that females have pulse rates that are normally distributed with a mean of u = 73.0 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 76 beats per minute. ts The probability is. (Round to four decimal places as needed.) b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute. The probability is . (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? OA. Since the distribution is of sample'means, not individuals, the distribution is a normal distribution for any sample size. O B. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. O C. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. Cinon the moon nulee roto ovnnode 30 the dictrihution of eomple moane in a normal dintrihition for anu emnle size Clis

Question Help v Assume that females have pulse rates that are normally distributed with a mean of u = 73.0 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 76 beats per minute. ts The probability is. (Round to four decimal places as needed.) b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean less than 76 beats per minute. The probability is . (Round to four decimal places as needed.) c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? OA. Since the distribution is of sample'means, not individuals, the distribution is a normal distribution for any sample size. O B. Since the distribution is of individuals, not sample means, the distribution is a normal distribution for any sample size. O C. Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size. Cinon the moon nulee roto ovnnode 30 the dictrihution of eomple moane in a normal dintrihition for anu emnle size Clis

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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