**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.

Note, since you posted multiple number of questions, we only provide the solution for first three…

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

See similar textbooks

Similar questions

The lifetime of a particular brand of AA batteries follows a normal distribution. The mean lifetime of particular brand of AA batteries is 1000 hours, with a standard deviation of 100 hours. What is the probability that a randomly selected battery lasts more than 875 hours? Select one: a. 0.8716 b. 0.3749 c. 0.1056 d. 0.8944
A population distribution has o =6. What position in this distribution is identified bya z-score = + 2.00?
Suppose that you are studying the number of vehicles owned by a US household. You find that the average is 1.9 vehicles per household with a standard deviation of 2.8 vehicles per household. What is the most likely shape for the population described above? Find the probability that 40 randomly selected households have an AVERAGE number of vehicles greater than 2.5.
The football coach randomly selected fifteen players and timed how long each player took to perform a certain drill. The times (in minutes) were: 3.5, 3.3, 3.2, 4.7, 4.4, 3.5, 3.9, 4.5, 4.8, 5.2, 5.4, 4.0, 4.3, 4.1, 5.1 (a) Show that this data approximates a normal distribution. (b) Determine a 90% confidence interval for the mean time for all players.
A biologist found the wingspans of a group of monarch butterflies to be normally distributed with a mean of 52.2 mm and a standard deviation of 2.3 mm. Find the probability of randomly selecting a value (Hint: round off z scores to 2 decimal places) 1. less than 48.5 mm? 2. between 50 mm and 55 mm?
the heights of 18-year old men are approximately normally distributed with a mean of U= 68 inches and a standard deviation of O=3. what is the probability that an 18-year-old mean selected at random is less than 65 inches tall. a .8413 b .1587 c .1389 d .8765
According to a study done by UCB students, the height for Martian adult males is normally distributed with an average of 64 inches and a standard deviation of 2.3 inches. Suppose one Martian adult male is randomly chosen. Let X = height of the individual. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. Find the probability that the person is between 62 and 63.9 inches. c. The middle 40% of Martian heights lie between what two numbers? Low: inches High: inches
Furnace repair bills are normally distributed with a mean of 271 dollars and a standard deviation of 20 dollars. If 64 of these repair bills are randomly selected, find the probability that they have a mean cost between 271 dollars and 273 dollars. Round to four decimal places. A. 0.2881 OB. 0.2119 O C. 0.5517 O D. 0.7881
In a local university, 80% of the students live in the dormitories. A random sample of 64 students is selected for a particular study. The standard deviation of p-bar is a. 64 b. 0.05 c. 1.6 d. 0.16 e. 0.5
1) The mean and standard deviation of a population are 200 and 20, respectively.The probability of selecting one data value less than 190 is ____ %. (Round answer to the nearest percent (whole number). Do not write the % sign.) 2) A. C. Neilsen reported that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours.If 20 children between the ages of 2 and 5 are randomly selected, the number of children in the sample who watch at least 25.2 hours of television is? Give answer to the nearest whole number, not a percent. 3) A. C. Neilsen reported that children between the ages of 2 and 5 watch an average of 25 hours of television per week. Assume the variable is normally distributed and the standard deviation is 3 hours.If 20 children between the ages of 2 and 5 are randomly selected, the number of children in the sample who watch at most 22.5 hours of television is? . Give…