Why do two normal distributions that have equal standard deviations have the same shape?

Answers (1)

2021-02-23

Step 1
In this case, we need to explain the reason for the two normal distribution with equal standard deviation have same shape.
Step 2
The normal distributions were bell shaped or symmetric about the population mean and the standard deviation states the square root of deviations about the mean. That is, spread from the mean. Thus, two normal distribution with equal standard deviation have same shape.

Relevant Questions

asked 2021-06-05

Use the following Normal Distribution table to calculate the area under the Normal Curve (Shaded area in the Figure) when \(Z=1.3\) and \(H=0.05\);
Assume that you do not have vales of the area beyond \(z=1.2\) in the table; i.e. you may need to use the extrapolation.
Check your calculated value and compare with the values in the table \([for\ z=1.3\ and\ H=0.05]\).
Calculate your percentage of error in the estimation.
How do I solve this problem using extrapolation?
\(\begin{array}{|c|c|}\hline Z+H & Prob. & Extrapolation \\ \hline 1.20000 & 0.38490 & Differences \\ \hline 1.21000 & 0.38690 & 0.00200 \\ \hline 1.22000 & 0.38880 & 0.00190 \\ \hline 1.23000 & 0.39070 & 0.00190 \\ \hline 1.24000 & 0.39250 & 0.00180 \\ \hline 1.25000 & 0.39440 & 0.00190 \\ \hline 1.26000 & 0.39620 & 0.00180 \\ \hline 1.27000 & 0.39800 & 0.00180 \\ \hline 1.28000 & 0.39970 & 0.00170 \\ \hline 1.29000 & 0.40150 & 0.00180 \\ \hline 1.30000 & 0.40320 & 0.00170 \\ \hline 1.31000 & 0.40490 & 0.00170 \\ \hline 1.32000 & 0.40660 & 0.00170 \\ \hline 1.33000 & 0.40830 & 0.00170 \\ \hline 1.34000 & 0.41010 & 0.00180 \\ \hline 1.35000 & 0.41190 & 0.00180 \\ \hline \end{array}\)

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asked 2020-11-29

When we want to test a claim about two population means, most of the time we do not know the population standard deviations, and we assume they are not equal. When this is the case, which of the following is/are not true?
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asked 2020-11-22

Answer true or false to each statement.
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b. Two normal distributions that have the same standard deviation have the same spread, regardless of the relationship between their means.

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asked 2020-11-01

Answer true or false to each statement. Explain your answers.
a. Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations.
b. Two normal distributions that have the same standard deviation have the same spread, regardless of the relationship between their means.

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asked 2020-12-15

Decide which of the following statements are true.
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asked 2020-10-27

Two normally distributed variables have the same means and the same standard deviations. What can say about their distributions?

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asked 2020-12-07

Suppose you take independent random samples from populations with means \(\displaystyle\mu{1}{\quad\text{and}\quad}\mu{2}\) and standard deviations \(\displaystyle\sigma{1}{\quad\text{and}\quad}\sigma{2}\). Furthermore, assume either that (i) both populations have normal distributions, or (ii) the sample sizes (n1 and n2) are large. If X1 and X2 are the random sample means, then how does the quantity
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asked 2021-02-26

Consider two normal distributions, one with mean-4 and standard deviation 3, and the other with mean 6 and standard deviation 3. Answer true or false to each statement and explain your answers.
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b. The two normal distributions are centered at the same place.

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asked 2020-12-01

True or false:
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asked 2021-01-28

There is a direct relationship between the chi-square and the standard normal distributions, whereby the square root of each chi-square statistic is mathematically equal to the corresponding z statistic at significance level \(\displaystyle\alpha\).
1.True
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