# Describe the basic steps that engineers follow to design something. Question
Modeling data distributions Describe the basic steps that engineers follow to design something. 2020-12-03
Step 1: The basic steps are Solution : The basic steps that engineers follow to design something 1. Design: The process of originating and developing a plan for a new object. This requires research , thought, modeling, interactive adjustment and re-design. 2. Identify the problem: Understand the scope and nature of the problem. Identify the correct issues and background of the problem. 3. Define working Criteria and goals: Establish primary Goals. Develop the working Criteria to compare the possible solutions i.e specification, constraints. 4.Research and gather Data: Stay consistence with working criteria while researching. Use resources to help the research including internet ,library newspaper. 5.Brainstorm and generate creative ideas: Develop as many as creative ideas as possible. No idea is a bad idea . Documents all ideas. If time permitted , hold a second session to give people time to consider additional option. Step 2: other steps 6. Analyze potential Solution: Eliminate duplicate ideas. Clarify ideas. Select ideas to analyze in more detail (qualitative analysis , Quantitative analysis, Democratic analysis) 7. Develop and Test Models: Develop models for the selected solution. If none of the solutions are ideal, return to stage 5 and 6 8.Make the Decision: Evaluate the results of testing to determine the solution to use. 9. Communicate and Specify: Document the design specification and measurement and communicate to all groups. 10. Implement and Commercialize: All groups should agree on the proposed project, including management, technical, and legal support representative. 11. Post-Implementation review and assessment: Reviews the products performance .Make suggestion for the future improvements.

### Relevant Questions 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. Describe the shape of a scatter plot that suggests modeling the data with an exponential function. Give a complete answer and describe Bayes' theorem In each of the following situations, the sampling frame does not match the population, resulting in undercoverage. Give example of population members that might have been omitted.
a) The population consists of all 250 students in your laege statistics class. You plan to obtain a sample random sample of 30 students by using the sample frame of students present next Monday.
b) The population consists of all 15-year-olds living in the attendance district of a local high school. You plna to obtain a simple random sample of 200 such residents by using the student roster of the high school as the sampling frame. M. F. Driscoll and N. A. Weiss discussed the modeling and solution of problems concerning motel reservation networks in “An Application of Queuing Theory to Reservation Networks” (TIMS, Vol. 22, No. 5, pp. 540–546). They defined a Type 1 call to be a call from a motel’s computer terminal to the national reservation center. For a certain motel, the number, X, of Type 1 calls per hour has a Poisson distribution with parameter $$\displaystyle\lambda={1.7}$$.
Determine the probability that the number of Type 1 calls made from this motel during a period of 1 hour will be:
a) exactly one.
b) at most two.
c) at least two.
(Hint: Use the complementation rule.)
d. Find and interpret the mean of the random variable X.
e. Determine the standard deviation of X. At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991. Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute. The resulting data were grouped by month of birth: January, May, and September: $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}&{C}{r}{a}{w}{l}\in{g}\ {a}\ge\backslash{h}{l}\in{e}{B}{i}{r}{t}{h}\ {m}{o}{n}{t}{h}&{M}{e}{a}{n}&{S}{t}.{d}{e}{v}.&{n}\backslash{h}{l}\in{e}{J}{a}\nu{a}{r}{y}&{29.84}&{7.08}&{32}\backslash{M}{a}{y}&{28.58}&{8.07}&{27}\backslash{S}{e}{p}{t}{e}{m}{b}{e}{r}&{33.83}&{6.93}&{38}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ Crawling age is given in weeks. Assume the data represent three independent simple random samples, one from each of the three populations consisting of babies born in that particular month, and that the populations of crawling ages have Normal distributions. A partial ANOVA table is given below. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{S}{o}{u}{r}{c}{e}&{S}{u}{m}\ {o}{f}\ \boxempty{s}&{D}{F}&{M}{e}{a}{n}\ \boxempty\ {F}\backslash{h}{l}\in{e}{G}{r}{o}{u}{p}{s}&{505.26}\backslash{E}{r}{r}{\quad\text{or}\quad}&&&{53.45}\backslash{T}{o}{t}{a}{l}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$ What are the degrees of freedom for the groups term? 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). $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{\left|{c}\right|}{c}{\mid}\right\rbrace}&{P}{\left({x}\right)}\backslash{L}{e}{f}{t}&{0.636}\backslash{R}{i}{g}{h}{t}&{0.304}\backslash{N}{o}\ {p}{r}{e}{f}{e}{r}{e}{n}{c}{e}&{0.060}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$   Listed below are amounts of strontium-90 (in millibecquerels or mBq per gram of calclum) in a simple random sample of baby teth obtained from resident of state A and state B. Use a 0.05 significance level to test the celm that amounts of Strontium-90 from state A residents vary more than amounts from state B resints. Assume that both samples are independent simple random samples from populations having normal distributions. $$\displaystyle{b}{e}{g}\in{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}{\left\lbrace{c}\right\rbrace}{S}{t}{a}{t}{e}{A}:&{162}&{143}&{150}&{130}&{152}&{152}&{143}&{155}&{131}&{139}&{164}\backslash{S}{t}{a}{t}{e}{B}:&{136}&{140}&{142}&{131}&{133}&{129}&{141}&{140}&{142}&{136}&{142}{e}{n}{d}{\left\lbrace{a}{r}{r}{a}{y}\right\rbrace}$$