# Data modeling questions and answers

Recent questions in Modeling data distributions
Modeling data distributions

### 1)What factors influence the correspondence between the binomial and normal distributions? 1.Twenty percent of individuals who seek psychotherapy will recover from their symptoms irrespective of whether they receive treatment. A research finds that a particular type of psychotherapy is successful with 30 out of 100 clients. Using an alpha level of 0.05 as a criterion, what should she conclude about the effectiveness of this psychotherapeutic approach? 2.How does the size of the data set help cut down on the size of the error terms in the approximation process?

Modeling data distributions

### An experiment designed to study the relationship between hypertension and cigarette smoking yielded the following data. $$\begin{array}{|c|c|} \hline Tension\ level & Non-smoker & Moderate\ smoker & Heavy\ smoker \\ \hline Hypertension & 20 & 38 & 28 \\ \hline No\ hypertension & 50 & 27 & 18 \\ \hline \end{array}$$ Test the hypothesis that whether or not an individual has hypertension is independent of how much that person smokes.

Modeling data distributions

### 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 $$= 1191.6, s = 506.6$$.]

Modeling data distributions

### Aurora is planning to participate in an event at her school's field day that requires her to complete tasks at various stations in the fastest time possible. To prepare for the event, she is practicing and keeping track of her time to complete each station. The x-coordinate is the station number, and the y-coordinate is the time in minutes since the start of the race that she completed the task. $$\displaystyle{\left({1},{3}\right)},{\left({2},{6}\right)},{\left({3},{12}\right)},{\left({4},{24}\right)}$$ Part A: Is this data modeling an algebraic sequence or a geometric sequence? Explain your answer. Part B: Use a recursive formula to determine the time she will complete station 5. Part C: Use an explicit formula to find the time she will complete the 9th station.

Modeling data distributions

### In general, the highest price p per unit of an item at which a manufacturer can sell N items is not constant but is, rather, a function of N. Suppose the manufacturer of widgets has developed the following table showing the highest price p, in dollars, of a widget at which N widgets can be sold. $$\begin{array}{|c|c|} \hline Number\ N & Price\ p\\ \hline 250 & 52.50\\ \hline300 & 52.00\\\hline 350 & 51.50\\ \hline 400 & 51.00\\ \hline \end{array}$$ (a) Find a formula for p in terms of N modeling the data in the table. $$\displaystyle{p}=$$ (b) Use a formula to express the total monthly revenue R, in dollars, of this manufacturer in a month as a function of the number N of widgets produced in a month. $$\displaystyle{R}=$$

Modeling data distributions

### Means $$=59.47444, SDS = 12.91711, Min = 23.599, Max = 82.603$$ AND Means $$= 67.00742, SDS = 12.7302, Min = 39.613, Max = 82.603$$ Means Based on your findings write a preliminary statistical report that comprises of the Methods, Results/Analysis and Conclusions sections. Include a comparison of the two distributions in (1) and (2) in terms of their central tendencies and variability. While your audience is one that lacks statistical expertise you are still expected to correctly interpret the data and statistical analyses, in a manner that is understandable to your audience. Be mindful to present an impartial report that distinguishes conclusive and inferential statements for the audience.

Modeling data distributions

### The volume of a sphere is given bby the equation $$\displaystyle{V}\ =\ {\frac{{{1}}}{{{6}\sqrt{{\pi}}}}}\ {S}^{{\frac{{3}}{{2}}}}$$, where S is the surface area of the sphere. Find the volume of a sphere, to the nearest cubic meter, that has a surface area of 60 square meter. Use 3.14 for $$\displaystyle\pi$$.

Modeling data distributions

### Find the limit, if it exists: $$\lim_{x \rightarrow \infty}(8+\frac{1}{x})$$

Modeling data distributions

### The formula $$\displaystyle{V}=\sqrt{{{P}{R}}}$$ relates the voltage V (in volts), power P (in watts), and resistance R (in ohms) of an electrical circuit. The hair dryer shown is on a 120-volt circuit. Is the resistance of the hair dryer half as much as the resistance of the same hair dryer on a 240-volt circuit? Explain your reasoning.

Modeling data distributions

### Explain Energy-based Definition.

Modeling data distributions

### There are several methods for system development such as Agile, XP, JAD and RUP. Identity any Two which you think are best for your case giving reasons

Modeling data distributions

### The attendances y for two movies can be modeled by the following equations, where x is the number of days since the movies opened. Movie A: $$\displaystyle{y}=-{x}^{{{2}}}+{35}{x}+{100}$$ Movie B: $$\displaystyle{y}=-{5}{x}+{275}$$ Where x is number of days since the movies opened. When is the attendance for each movie the same?

Modeling data distributions

### Suppose \$10,000 is invested at an annual rate of $$\displaystyle{2.4}\%$$ for 10 years. Find the future value if interest is compounded as follows

Modeling data distributions

### Solve and give the correct answer with using second derivative of the function as follows $$\displaystyle f{{\left({x}\right)}}={\left({x}+{9}\right)}^{2}$$

Modeling data distributions

### Find an exponential function that fits the experimental data collected over time t. \begin{array}{|c|c|} \hline t & 0 & 1 & 2 & 3 & 4 \\ \hline y & 600.00 & 630.00 & 661.50 & 694.58 & 729.30 \\ \hline \end {array}

Modeling data distributions

### The admissions office of a college wants to determine whether there is a relationship between IQ scores x and grade-point averages y after the first year of school. An equation that models the data obtained by the admissions office is $$\displaystyle{y}={0.069}{x}-{4.755}.$$ Estimate the values of x that predict a grade-point average of at least 3.5. (Simplify your answer completely. Round your answer to the nearest whole number.)

Modeling data distributions

### What is the difference between a normal profile of a random variable and normal pdf of a random variable. What is the median value of a random variable having a normal pdf.

Modeling data distributions

### Use the change-of-base theorem to find an approximation to four decimal places for each logarithm $$\displaystyle{{\log}_{{2}}{5}}$$

Modeling data distributions