Answered: With the new mean and standard…

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

Question 4- Already Answered- See Question 5

After some time has passed, all of the chickens lay full-sized eggs. (When chickens first start laying, many of their eggs are small.) So, the mean weight goes up to 24 ounces. At the same time, the variation decreases, so the standard deviation goes down to 2 ounces.

Mark off a normal distribution with the numbers for the mean and each deviation by labeling the values for A, B, C, D, E, F, and G in the table.

	Value
A
B
C
D
E
F
G

Expert Solution

arrow_forward

Step 1

A normal distribution is a continuous probability distribution that makes a bell-shaped curve of the data. It creates a symmetric distribution with the mean, median, and mode at the center of the graph where mean=median=modemean=median=mode.

According to empirical rule, 99.7% of normally distributed data lies within 3 standard deviations from the mean value (μ±3σμ±3σ).

The data in the normal distribution would be:

μ±1σ=68%μ±2σ=95%μ±3σ=99.7%μ±1σ=68%μ±2σ=95%μ±3σ=99.7%

arrow_forward

Step 2

Answer 4.

In this study, the data of chickens' eggs size was normally distributed with a mean (μ=24 ouncesμ=24 ounces) and the standard deviation (σ=2 ouncesσ=2 ounces).

According to the Empirical, if the data is following the normal distribution, 99.7% of data seen following a normal distribution falls within three standard deviations of the mean. According to this criteria, one standard deviation away from the mean includes 68% of data, two standard deviations away from the mean includes 95% of data, and within three standard deviations from the mean includes 99.7% of data.

The data would be distributed in the following manner

μ±1σ=68%μ±2σ=95%μ±3σ=99.7%μ±1σ=68%μ±2σ=95%μ±3σ=99.7%

The table calculation would be:

A=μ−3σB=μ−2σC=μ−1σD=μ+0σE=μ+1σF=μ+2σG=μ+3σA=μ-3σB=μ-2σC=μ-1σD=μ+0σE=μ+1σF=μ+2σG=μ+3σ

The table shows the calculation and value of egg size in a normal distribution table:

	Calculation	Value
A	=24−3×2=24-3×2	18
B	=24−2×2=24-2×2	20
C	=24−1×2=24-1×2	22
D	=24+0×2=24+0×2	24
E	=24+1×2=24+1×2	26
F	=24+2×2=24+2×2	28
G	=24+3×2=24+3×2	30

The table showed that data would be distributed in a range from 18 ounces to 30 ounces within 3 three standard deviations from the mean. It means that 99.7% of egg size would fall between 24 and 34 ounces in a normal distribution table.

Question 5 is the one I need assistance with.

Question 5

With the new mean and standard deviation, how many standard deviations away from the mean is the value of 18.5 ounces? Is the value above or below the mean?

Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.

Expert Solution