Use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the functionp(x)=\frac{1}{\sqrt{2\pi^\sigma}}e-(x-\mu)^2/(2\sigma^2)

aflacatn 2021-08-04 Answered

This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function
\(\displaystyle{p}{\left({x}\right)}={\frac{{{1}}}{{\sqrt{{{2}\pi^{\sigma}}}}}}{e}-\frac{{\left({x}-\mu\right)}^{{2}}}{{{2}\sigma^{{2}}}}\)
where \(\pi\) = 3,14159265 ... and \(\sigma\) and \(\mu\) are constants called the standard deviation and the mean, respectively. Its graph (for \(\sigma=1\) and \(\mu=2)\) is shown in the figure.
With \(\displaystyle\sigma={\color{red}{{5}}}\) and \(\mu=0\), approximate \(\displaystyle{\int_{{{0}}}^{{+\infty}}}{p}{\left({x}\right)}{\left.{d}{x}\right.}\).(Round your answer to four decimal places.)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Tobias Ali
Answered 2021-08-10 Author has 23218 answers

Step 1
Here, \(x\sim=N(M,\sigma^2)\)
To find \( \int_{0}^{+oo} p(x)dx, 10\) here \(\int_{}^{}(x)=\frac{1}{\sigma\sqrt{2K}}e^(x-\mu)^2/2\sigma^2,x\in R\)
\( \int_{}^{}(x)\)is the PDF of x
\(\displaystyle\Rightarrow{\int_{{{0}}}^{{+\infty}}}{\int_{{\lbrace}}^{{\lbrace}}}{\left({x}\right)}{\left.{d}{x}\right.}={P}{\left[{x}{>}{0}\right]}\)
\(\displaystyle{x}\sim{N}{\left({M},\sigma^{{2}}\right)}\Rightarrow{\frac{{{x}-{M}}}{{\sigma}}}\sim{N}{\left({0},{1}\right)}\)
\(\displaystyle{F}{\quad\text{or}\quad}{M}={0},\sigma={5}{M}={\frac{{{x}}}{{{5}}}}\sim{N}{\left({0},{1}\right)}\)
\(\displaystyle{T}{h}{e}{n},{P}{\left[{x}{>}{0}\right]}={P}{\left[{\frac{{{x}}}{{{5}}}}{>}{0}\right]}+{P}{\left[{y}{>}{0}\right]}\)
\(\displaystyle={1}-{P}{\left[{y}\leq{0}\right]}={1}-\phi{\left({0}\right)}\)
\(\displaystyle={1}-{0}\cdot{5}={0}\cdot{5}\) Step 2 Hence,the required value is 0.5.

Not exactly what you’re looking for?
Ask My Question
16
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-01-31
This exercise requires the use of a graphing calculator or computer programmed to do numerical integration. The normal distribution curve, which models the distributions of data in a wide range of applications, is given by the function \(p(x)=\frac{1}{\sqrt{2 \pi}^{\sigma}}e^{-(x-\mu)^{2}}/(2 \sigma^{2})\) where \(\pi = 3.14159265 . . .\) and sigma and mu are constants called the standard deviation and the mean, respectively. Its graph\((\text{for}\ \sigma=1\ \text{and}\ \mu=2)\)is shown in the figure. With \(\sigma = 5 \text{and} \mu = 0\), approximate \(\int_0^{+\infty}\ p(x)\ dx.\)
asked 2021-06-09

The following table represents the Frequency Distribution and Cumulative Distributions for this data set: 12, 13, 17, 18, 18, 24, 26, 27, 27, 30, 30, 35, 37, 41, 42, 43, 44, 46, 53, 58

\(\begin{array}{|c|c|} \hline \text{Class}&\text{Frequency}&\text{Relative Frequency}&\text{Cumulative Frequency}\\ \hline \text{10 but les than 20}&5\\ \hline \text{20 but les than 30}&4\\ \hline \text{30 but les than 40}&4\\ \hline \text{40 but les than 50}&5\\ \hline \text{50 but les than 60}&2\\ \hline \text{TOTAL}\\ \hline \end{array}\)

What is the Relative Frequency for the class: 20 but less than 30? State you answer as a value with exactly two digits after the decimal. for example 0.30 or 0.35

asked 2020-11-30

Identifying Probability Distributions. In Exercises 7–14, determine whether a probability distribution is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied. Cell Phone Use In a survey, cell phone users were asked which ear they use to hear their cell phone, and the table is based on their responses (based on data from “Hemispheric Dominance and Cell Phone Use,” by Seidman et al., JAMA Otolaryngology—Head & Neck Surgery , Vol. 139, No.

5). \(\begin{array}{|c|c|}& P(x)\\ Left & 0.636 \\ Right & 0.304 \\ No\ preference & 0.060\end{array}\)

asked 2021-08-08

Presenting data in the form of table. For the data set shown by the table, Solve,
a) Create a scatter plot for the data.
b) Use the scatter plot to determine whether an exponential function, a logarithmic function, or a linear function is the best choice for modeling the data. (If applicable, you will use your graphing utility to obtain these functions.)
\(\begin{array}{|c|c|}\hline \text{Intensity (wattd per}\ meter^{2}) & \text{Loudness Level (decibels)} \\ \hline 0.1\text{(loud thunder)} & 110 \\ \hline 1\text{(rock concert, 2 yd from speakers)} & 120 \\ \hline 10 \text{(jackhammer)} & 130 \\ \hline 100 \text{(jet take off, 40 yd away)} & 140 \\ \hline \end{array}\)

asked 2021-01-19

Which possible statements about the chi-squared distribution are true?
a) The statistic \(X^{2}\), that is used to estimate the variance \(S^{2}\) of a random sample, has a Chi-squared distribution.
b) The sum of the squares of k independent standard normal random variables has a Chi-squared distribution with k degrees of freedom.
c) The Chi-squared distribution is used in hypothesis testing and estimation.
d) The Chi-squared distribution is a particular case of the Gamma distribution.
e)All of the above.

asked 2021-03-02

The following observations are lifetimes (days) subsequent to diagnosis for individuals suffering from blood cancer ("A Goodness of Fit Approach to the Class of Life Distributions with Unknown Age," Quality and Reliability Engr. Intl., \(2012: 761-766): 115, 181, 255, 418, 441, 461, 516, 739, 743, 789, 807, 865, 924, 983, 1025, 1062, 1063, 1165, 1191, 1222, 1222, 1251, 1277, 1290, 1357, 1369, 1408, 1455, 1278, 1519, 1578, 1578, 1599, 1603, 1605, 1696, 1735, 1799, 1815, 1852, 1899, 1925, 1965.\)
a) can a confidence interval for true average lifetime be calculated without assuming anything about the nature of the lifetime distribution? Explain your reasoning. [Note: A normal probability plot of data exhibits a reasonably linear pattern.]
b) Calculate and interpret a confidence interval with a 99% confidence level for true average lifetime. [Hint: mean \(= 1191.6, s = 506.6\).]

asked 2021-01-17

Use the table from the Theoretical Distribution section to calculate the following answers. Round your answers to four decimal places. \(P(x = 3)=?\)
\(P(1 < x < 4) = ?\)
\(P(x \geq 8) = ?\) Use the data from the Organize the Data section to calculate the following answers. Round your answers to four decimal places. \(RF(x = 3) = ?\)
\(RF(1 < x < 4) =?\)
\(RF(x \geq 8) = ?\) Discussion Questions 1. Knowing that data vary, describe three similarities between the graphs and distributions of the theoretical, empirical, and simulation distributions. Use complete sentences.

...