Explain some of the important characteristics of a normal distribution.

Answers (1)

2021-03-09

When number of trials of an experiment increases, and then the probability distribution curve becomes smoother and reaches a bell-shaped curve which is called as normal distribution. Some of the important characteristics of normal distribution are listed below.
-The area under any normal distribution must be equal to 1.
-Normal distribution is always symmetrical about the mean.
Conclusion:
Thus, some of the important characteristics of a normal distribution have been explained.

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?
\(\begin{array}{|c|c|}\hline Z+H & Prob. & Extrapolation \\ \hline 1.20000 & 0.38490 & Differences \\ \hline 1.21000 & 0.38690 & 0.00200 \\ \hline 1.22000 & 0.38880 & 0.00190 \\ \hline 1.23000 & 0.39070 & 0.00190 \\ \hline 1.24000 & 0.39250 & 0.00180 \\ \hline 1.25000 & 0.39440 & 0.00190 \\ \hline 1.26000 & 0.39620 & 0.00180 \\ \hline 1.27000 & 0.39800 & 0.00180 \\ \hline 1.28000 & 0.39970 & 0.00170 \\ \hline 1.29000 & 0.40150 & 0.00180 \\ \hline 1.30000 & 0.40320 & 0.00170 \\ \hline 1.31000 & 0.40490 & 0.00170 \\ \hline 1.32000 & 0.40660 & 0.00170 \\ \hline 1.33000 & 0.40830 & 0.00170 \\ \hline 1.34000 & 0.41010 & 0.00180 \\ \hline 1.35000 & 0.41190 & 0.00180 \\ \hline \end{array}\)

See answers (1)

asked 2021-05-18

The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below:
Robert, 1.10 Juan, 1.70 Susan, -2.00
Joel, 0.00 Jan, -0.80 Linda, 1.60
Which of these students scored above the mean?

See answers (1)

asked 2021-05-09

The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were normally distributed, and the z scores for some of the students are shown below:
Robert, 1.10 Juan, 1.70 Susan, -2.00
Joel, 0.00 Jan, -0.80 Linda, 1.60
Which of these students scored above the mean?

See answers (1)

asked 2021-02-22

The normal distribution is really a family of distributions. Is the standard normal distribution also a family of distributions?Explain.

See answers (1)

asked 2021-05-03

Describe in words the surface whose equation is given. (assume that r is not negative.) \(\theta=\frac{\pi}{4}\)
a) The plane \(y = −z\) where y is not negative
b) The plane \(y = z\) where y and z are not negative
c) The plane \(y = x\) where x and y are not negative
d) The plane \(y = −x\) where y is not negative
e) The plane \(x = z\) where x and y are not negative

See answers (1)

asked 2020-11-17

Which would you expect to have a density curve that is higher at the mean: the standard normal distribution or a normal distribution with standard deviation 0.5? Explain.

See answers (1)

asked 2021-02-25

Explain why t distributions tend to be flatter and more spread out than the normal distribution.

See answers (1)

asked 2021-06-15

The missing number in the series 1, 4, 27,____, 3125 is: 81 35 729 256 115

See answers (1)

asked 2021-02-27

The manager of the store in the preceding exercise calculated the residual for each point in the scatterplot and made a dotplot of the residuals.
The distribution of residuals is roughly Normal with a mean of $0 and standard deviation of $22.92.
The middle 95% of residuals should be between which two values? Use this information to give an interval of plausible values for the weekly sales revenue if 5 linear feet are allocated to the store's brand of men's grooming products.

See answers (1)

asked 2021-03-04

Consider the marks of all 1st-year students on a statistics test. If the marks have a normal distribution with a mean of 72 and a standard deviation of 9, then the probability that a random sample of 10 students from this group have a sample mean between 71 and 73 is?

See answers (1)

You might be interested in

The ___________ relative frequencies are the sums of each row and column in a two-way table. (joint, marginal, or conditional)

For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the da

You randomly survey shoppers at a supermarket about whether they use reusable bags. Of 60 male shoppers 15 use reusable bags. Of 110 female shoppers,

The college physical education department offered an advanced first aid course last semester. The scores on the comprehensive final exam were normally

An observational study is retrospective if it considers only existing data. It is prospective if the study design calls for data to be collected as ti

You randomly survey students in your school about whether they have a pet. You display your results in the two-way table. How many female students too

Assume that all the distributions are normal, average is always taken to be the arithmetic mean xˉ or μ. A college Physical Education Department offer

For what types of variables, quantitative or qualitative, are scatterplots useful?

Painful bone metastases are common in advanced prostate cancer. Physicians often order treatment with strontium-89 (89Sr), a radionuclide with a stron

The missing number in the series 1, 4, 27,____, 3125 is: 81 35 729 256 115

Painful bone metastases are common in advanced prostate cancer. Physicians often order treatment with strontium-89 (89Sr), a radionuclide with a stron

Is it true that girls perform better than boys in the study of languages and so-called soft sciences? Here are several Advanced Placement subjects and

...