Question Solved1 Answer Among fatal plane crashes that occurred during the past 50 years, 271 were due to pilot error, 81 were due to other human error, 183 were due to weather, 487 were due to mechanical problems, and 202 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it? Among fatal plane crashes that occurred during the past 50 years, 271 were due to pilot error, 81 were due to other human error, 183 were due to weather, 487 were due to mechanical problems, and 202 were due to sabotage. Construct the relative frequency distribution. What is the most serious threat to aviation safety, and can anything be done about it? Complete the relative frequency distribution below. Cause Relative Frequency % Pilot error Other human error % Weather % Mechanical problems % Sabotage 1% (Round to one decimal place as needed.) What is the most serious threat to aviation safety, and can anything be done about it? O A. Weather is the most serious threat to aviation safety. Weather monitoring systems could be improved. O B. Sabotage is the most serious threat to aviation safety. Airport security could be increased. O C. Mechanical problems are the most serious threat to aviation safety. New planes could be better engineered. O D. Pilot error is the most serious threat to aviation safety. Pilots could be better trained.

You perform a clinical trial to study new drug. You have 20 volunteers with some disease. You randomly split all the volunteers into two groups (10 volunteers in each): the treatment group and the control group. Volunteers in the treatment group receive the new drug, volunteers in the control group receive placebo (pills that looks like a drug but do not have active substance). You conclude that new drug is effective if people who take the drug will recover faster (on average) than people in the control group. If your drug is effective, you will invest in its production, otherwise you will look for another drug. Assume that you obtained the following data (disease duration in days). control group treatment group 6 7 7 6 7 6 5 5 7 5 8 6 8 7 7 5 7 5 7 8 Describe this problem in terms of statistical hypothesis testing framework. How would you model your data in terms of random variables? State the null hypothesis and the alternative. Will your alternative be one-sided or two-sided? Why? What kind of statistical test will you use? Why this test? Use this test (apply Python if necessary and provide your code), analyse the results and provide a conclusion in mathematical and real-life terms. Would you invest into production of this drug?

Multiple choice, pick one ans: Consider the grammar G S ::= aS | T T ::= bT | U U ::= cU | ϵ (1) Which of the following strings is generated by the grammar G? (a) aba (b) bab (c) ca (d) ccc (2) Which of the following is a derivation of bbc in the grammar G? (a) S → T → U → bU → bbU → bbU → bbc (b) S → bT → bbT → bbU → bbcU → bbc (c) S → T → bT → bbT → bbU → bbcU → bbc (d) S → T → bT → bTbT → bbT → bbU → bbcU → bbc (3) Which of the following grammars describes the same language as 0^m1^n where m ≤ n? (a) S ::= 0S1 | ϵ (b) S ::= 0S1 | S1 | ϵ (c) S ::= 0S1 | 0S | ϵ (d) S ::= SS | 0 | 1 | ϵ

3. Recall that x a f x f a f xx a − −  = → ( ) ( ) ( ) lim or h f a h f a h ( ) ( ) lim 0 + − →(a) If f x x ( ) 1 = + , find f (a) using the formula of yourchoice. Show all steps. (b) Find the equation of the tangent lineto f (x) at x = 3. 3. Recall that f'(x) = lim(x) - f(a) or lim f(a+h)-f(a) + X-a 0 h (a) If f(x) = Vx+1, find f'(a) using the formula of your choice. Show all steps. (b) Find the equation of the tangent line to f(x) at x = 3.

5. Lisa James expects to retire in fifteen years and she expects to live ten years after she retires. Lisa would like to have \( \$ 20,000 \) available at the beginning of each year of her retirement. How much would Lisa need to deposit at the end of each of the next ten years in order for her to reach her retirement objective? The deposits will be made into 5. Lisa James expects to retire in fifteen years and she expects to live ten years after she retires. Lisa would like to have \( \$ 20,000 \) available at the beginning of each year of her retirement. How much would Lisa need to deposit at the end of each of the next ten years in order for her to reach her retirement objective? The deposits will be made into an account that earns \( 10 \% \) interest. \( \$ 5,266.63 \) \( \begin{array}{lc}P V=\frac{F V}{(1+i)^{n}} & F V=P V(1+i)^{n} \\ P V A=\frac{P M T}{i}\left[1-\frac{1}{(1+i)^{n}}\right] & F V A=\frac{P M T}{i}\left[(1+i)^{n}-1\right] \\ P V A_{D U E}=\frac{P M T}{i}\left[1-\frac{1}{(1+i)^{n}}\right](1+i) & F V A_{D U E}=\frac{P M T}{i}\left[(1+i)^{n}-1\right](1+i) \\ P V G A=\frac{P M T}{i-g}\left[1-\frac{(1+g)^{n}}{(1+i)^{n}}\right] & F V G A=\frac{P M T}{i-g}\left[(1+i)^{n}-(1+g)^{n}\right] \\ E P R=\frac{A P R}{m} & E P R=(1+E A R)^{\frac{1}{m}}-1 \\ E A R=\left(1+\frac{A P R}{m}\right)^{m}-1 & \end{array} \)

Question 2 (1 point) Salary information regarding male and female employees of a large company is shown below. Male Female Sample Size 64 36 Sample Mean Salary (in $1000) 45 41 Population Variance (2) 128 72 At 95% confidence, the margin of error is 1.960. 01.645 3.920. 7.839.

The following table reports real GDP per person for several different economies in the years 1960 and 2010. It also gives each economy's average annual growth rate during this period. For example, real GDP per person in the Central African Republic was $1,010 in 1960, and it actually declined to $628 by 2010. The Central African Republic's average annual growth rate during this period was -0.95%, and it was the poorest economy in the table in the year 2010. The real GDP-per-person figures are denominated in U.S. dollars with a base year of 2005. The following exercises will help you to understand the different growth experiences of these economies. 1. Economic growth around the worldThe following table reports real GDP per person for several different economies in the years 1960 and 2010. It also gives each economy's averageannual growth rate during this period. For example, real GDP per person in the Central African Republic was $1,010 in 1960, and it actuallydeclined to $628 by 2010. The Central African Republic's average annual growth rate during this period was -0.95%, and it was the poorest economyin the table in the year 2010.The real GDP-per-person figures are denominated in U.S. dollars with a base year of 2005. The following exercises will help you to understand thedifferent growth experiences of these economies.Real GDP per Person in 1960Real GDP per Person in 2010 Annual Growth RateEconomy(Dollars)(Dollars)(Percent)Australia13,81737,3382.01Finland8,83731,6012.58Thailand7728,4674.91Ireland7,80741,5583.40Pakistan7172,4772.51Central African Republic1,010628-0.95Indicate which economy satisfies each of the following statements.Central AfricanRepublicStatementAustraliaFinlandIrelandPakistanThailandThis economy experienced the fastest rate of growth in realGDP per person from 1960 to 2010.This economy had the highest level of real GDP per person inthe year 2010.Consider the following list of four countries. Which economy began with a level of real GDP per person in 1960 that was below that of Finland and grewfast enough to catch up with and surpass Finland's real GDP per person by 2010?AustraliaO Central African RepublicO IrelandPakistan