You work for a consumer watchdog publication and are testing the advertising claims of a tire manufacturer. The manufacturer claims that the life spans of the tires are normally distributed, with a mean of 40,000 miles and a standard deviation of 4500 miles. You test 16 tires and get the following life spans. Complete parts (a) through (c) below.48,250, 43,242, 27,538, 38,187, 30,583, 40,298, 40,623, 35,366, 24,131, 33,680, 38,592, 36,796, 32,216, 37,370, 36,319, 47,459Draw a frequency histogram to display these data. Use five classes. Then choose the from a, b, or c, for the correct answer below. The image contains three histograms labeled "a," "b," and "c," depicting the life spans of tires. Each histogram illustrates the frequency distribution of tire mileage, where:- The x-axis represents the mileage range from 26,542.5 to 45,338.5.- The y-axis represents frequency, ranging from 1 to 6.Details of each histogram:**a.** - Shows a distribution with varying frequencies.- The highest bar (frequency 6) is situated in the central mileage range.- Other bars show a descending frequency pattern towards the lower and higher mileage ranges.**b.**- Displays a more symmetrical distribution, resembling a bell shape (normal distribution).- The central mileage range has the highest frequency (6).- Frequencies taper off symmetrically towards both ends.**c.**- Similar to histogram "b" with a central peak.- The highest frequency (6) is in the middle mileage range.- Frequencies decrease towards the ends, indicating a symmetric pattern.These histograms help visualize and compare the distribution of tire life spans across different mileage categories.

The given data is 24131, 27538, 30583, 32216, 33680, 35366, 36319, 36796, 37370, 38187, 38592, 40298, 40623, 43242, 47459, 48250Solution : Arrange the given data in ascending order : 24131, 27538, 30583, 32216, 33680, 35366, 36319, 36796, 37370, 38187, 38592, 40298, 40623, 43242, 47459, 48250 Class width = (Maximum - Minimum) /number of classes = (28250-24131)/5 = 4823.8 = 4824 Frequency distribution table : Classes Frequencies 24131 - 28954 2 28955 - 33778 3 33779 - 38602 6 38603 - 43426 3 43427 - 48250 2 From the above frequency distribution, the correct answer for graph is option BAnswer - option B

Answered: You work for a consumer watchdog…

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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You work for a consumer watchdog publication and are testing the advertising claims of a tire manufacturer. The manufacturer claims that the life spans of the tires are normally distributed, with a mean of 40,000 miles and a standard deviation of 4500 miles. You test 16 tires and get the following life spans. Complete parts (a) through (c) below.

48,250, 43,242, 27,538, 38,187, 30,583, 40,298, 40,623, 35,366, 24,131, 33,680, 38,592, 36,796, 32,216, 37,370, 36,319, 47,459

Draw a frequency histogram to display these data. Use five classes. Then choose the from a, b, or c, for the correct answer below.

The image contains three histograms labeled "a," "b," and "c," depicting the life spans of tires. Each histogram illustrates the frequency distribution of tire mileage, where:

- The x-axis represents the mileage range from 26,542.5 to 45,338.5.
- The y-axis represents frequency, ranging from 1 to 6.

Details of each histogram:

**a.**
- Shows a distribution with varying frequencies.
- The highest bar (frequency 6) is situated in the central mileage range.
- Other bars show a descending frequency pattern towards the lower and higher mileage ranges.

**b.**
- Displays a more symmetrical distribution, resembling a bell shape (normal distribution).
- The central mileage range has the highest frequency (6).
- Frequencies taper off symmetrically towards both ends.

**c.**
- Similar to histogram "b" with a central peak.
- The highest frequency (6) is in the middle mileage range.
- Frequencies decrease towards the ends, indicating a symmetric pattern.

These histograms help visualize and compare the distribution of tire life spans across different mileage categories.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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