**Probability and Normal Distribution in Survey of Heights**In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.4 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below.### (a) Probability of a Height Less Than 67 InchesThe first task is to determine the probability that a study participant has a height that is less than 67 inches. **Solution:**The probability that the study participant selected at random is less than 67 inches tall is $ \boxed{} $. (Round to four decimal places as needed.)### (b) Probability of Height Between 67 and 72 InchesNext, we need to find the probability that a study participant has a height that is between 67 and 72 inches.**Solution:**The probability that the study participant selected at random is between 67 and 72 inches tall is $ \boxed{} $. (Round to four decimal places as needed.)### (c) Probability of a Height Greater Than 72 InchesWe then determine the probability that a study participant has a height that is more than 72 inches.**Solution:**The probability that the study participant selected at random is more than 72 inches tall is $ \boxed{} $. (Round to four decimal places as needed.)### (d) Identification of Unusual EventsFinally, identify any unusual events and explain the reasoning. Choose the correct answer below.**Solution:****A.** The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.---This exercise helps in understanding the application of normal distribution to real-life scenarios, such as the distribution of heights in a given population. By mastering these concepts, students can develop strong analytical and problem-solving skills in statistics and probability.

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In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.4 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than 67 inches tall is (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 67 and 72 inches. The probability that the study participant selected at random is between 67 and 72 inches tall is (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 72 inches. The probability that the study participant selected at random is more than 72 inches tall is (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. O A. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.

In a survey of a group of men, the heights in the 20-29 age group were normally distributed, with a mean of 67.4 inches and a standard deviation of 4.0 inches. A study participant is randomly selected. Complete parts (a) through (d) below. (a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than 67 inches tall is (Round to four decimal places as needed.) (b) Find the probability that a study participant has a height that is between 67 and 72 inches. The probability that the study participant selected at random is between 67 and 72 inches tall is (Round to four decimal places as needed.) (c) Find the probability that a study participant has a height that is more than 72 inches. The probability that the study participant selected at random is more than 72 inches tall is (Round to four decimal places as needed.) (d) Identify any unusual events. Explain your reasoning. Choose the correct answer below. O A. The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.

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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