## Probability and Statistics: Elevator Safety Analysis### Problem StatementAn elevator has a placard indicating that the maximum capacity is 2505 lbs for 15 passengers. Given this information, we want to determine the safety of the elevator under the following conditions:1. **Maximum Mean Weight per Passenger**: 167 lbs (calculated as 2505 lbs / 15 passengers).2. **Given Parameters**: - The elevator is loaded with 15 adult male passengers. - The mean weight of adult males is 174 lbs. - The standard deviation of adult male weights is 25 lbs.### ObjectiveFind the probability that the elevator is overloaded given the mean and standard deviation of the weights of adult males. Use this probability to assess if the elevator appears to be safe.### TaskCalculate the probability that the average weight of the 15 passengers exceeds 167 lbs. Use a normal distribution approach, given the following assumptions:- The weights of males are normally distributed.### Instructions1. **Input the final answer for the probability**: Enter the probability as a decimal rounded to four decimal places.2. **Verify and check your answer**: Use the input box provided to enter your answer, then click "Check Answer" to validate your calculation.![Probability Calculation Interface](https://via.placeholder.com/800x400)### Calculation StepsTo approach this problem, follow these steps using statistical methods:1. **Standardize the Problem**: - Calculate the standard error of the mean (SEM) for the 15 passengers: \( \text{SEM} = \frac{\sigma}{\sqrt{n}} \), where \(\sigma = 25\) lbs, and \(n = 15\). 2. **Determine the Z-score**: - Find the z-score for the threshold weight (167 lbs) using the formula: \[ Z = \frac{X - \mu}{\text{SEM}} \] where \(X = 167\) lbs, and \(\mu = 174\) lbs.3. **Calculate the Probability**: - Use the Z-score to find the corresponding probability from a standard normal distribution table.4. **Interpret the Result**: - Based on the calculated probability, assess if the probability of exceeding the threshold indicates that the elevator is likely unsafe.### NoteThis exercise helps understand the application of normal distribution in

An elevator has a placard stating that the maximum capacity is 2505 Ib-15 passengers. So, 15 adult male passengers can have a mean weight of up to 2505 /15 = 167 pounds. If the elevator is loaded with 15 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 167 Ib. (Assume that weights of males are normally distributed with a mean of 174 Ib and a standard deviation of 25 lb.) Does this elevator appear to be safe? The probability the elevator is overloaded is. (Round to four decimal places as needed.)

An elevator has a placard stating that the maximum capacity is 2505 Ib-15 passengers. So, 15 adult male passengers can have a mean weight of up to 2505 /15 = 167 pounds. If the elevator is loaded with 15 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 167 Ib. (Assume that weights of males are normally distributed with a mean of 174 Ib and a standard deviation of 25 lb.) Does this elevator appear to be safe? The probability the elevator is overloaded 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

See similar textbooks

Similar questions

A particular fruit's weights are normally distributed, with a mean of 696 grams and a standard deviation of 25 grams. If you pick 26 fruits at random, then 4% of the time, their mean weight will be greater than how many grams? Give your answer to the nearest gram.
In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 74 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. The lowest score that would qualify a student for an A is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a B is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a C is nothing. (Round up to the nearest integer as needed.) The lowest score that would qualify a student for a D is nothing. (Round up to the nearest integer as needed.)
Based on data from the National Health Board, weights of men are normally distributed with a mean of 178 lbs, and a standard deviation of 29 lbs. Find the probability that 20 randomly selected men will have a mean weight between 170 and 190.
A particular fruit's weights are normally distributed, with a mean of 636 grams and a standard deviation of 18 grams.If you pick 21 fruits at random, then 15% of the time, their mean weight will be greater than how many grams?
A particular fruit's weights are normally distributed, with a mean of 453 grams and a standard deviation of 28 grams. If you pick 10 fruits at random, then 12% of the time, their mean weight will be greater than how many grams?
Jeremiah earned a score of 530 on Exam A that had a mean of 450 and a standard deviation of 40. He is about to take Exam B that has a mean of 63 and a standard deviation of 20. How well must Jeremiah score on Exam B in order to do equivalently well as he did on Exam A? Assume that scores on each exam are normally distributed.
In a large section of a statistics class, the points for the final exam are normally distributed, with a mean of 73 and a standard deviation of 8. Grades are assigned such that the top 10% receive A's, the next 20% received B's, the middle 40% receive C's, the next 20% receive D's, and the bottom 10% receive F's. Find the lowest score on the final exam that would qualify a student for an A, a B, a C, and a D. Click here to view Page 1 of the Standard Normal Table. Click here to view Page 2 of the Standard Normal Table. The lowest score that would qualify a student for an A is (Round up to the nearest integer as needed.)
An elevator has a play card stating that the maximum capacity is 1980 pounds 12 passengers so 12 adult male passages can have a mean way of up to 1180÷12 = 165 pounds. If the elevator is loaded with 12 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 165 lb. Assume that weights of males are normally distributed with a mean of 172 pounds and a standard deviation of 27 pounds. Does this elevator appear to be safe?
Suppose that you are designing an instrument panel for a large industrial machine. The machine requires the person using it to reach 2 feet from a particular position. The reach from this position for adult women is known to have a mean of 2.7 feet with a standard deviation of 0.5. The reach for adult men is known to have a mean of 3.1 feet with a standard deviation of 0.7. Both women's and men's reach from this position is normally distributed. If this design is implemented, (a) what percentage of women will not be able to work on this instrument panel? (b) What percentage of men will not be able to work on this instrument panel? (c) Explain your answers to a person who has never had a course in statistics. Click here to view page 1 of the table. Click here to view page 2 of the table. Click here to view page 3 of the table. Click here to view page 4 of the table.
A particular fruit's weights are normally distributed, with a mean of 701 grams and a standard deviation of 30 grams.If you pick 24 fruits at random, then 2% of the time, their mean weight will be greater than how many grams?Give your answer to the nearest gram.
The length of the western rattlesnake is normally distributed with a mean of 42 inches and a standard deviation of 2.04 inches. Let X be the length of one of these snakes selected at random. Determine the probability that the snake is longer than 45 inches. Report your answer to four decimal places (like .1567).