Write a script YourLastName$\_$HW$6.$m$,$ which will simulate and analyze the electrical power produced by a wind turbine. The turbine generates power according to the following formula:

$Pwr=0\mathrm{.}5*A***(v_{\text{w}\text{i}\text{n}\text{d}}{)}^3$

Pwr $-$ turbine power $($in W$),v_{\text{w}\text{i}\text{n}\text{d}}-$ wind velocity $(\frac{m}{s}),=1\mathrm{.}225k\frac{g}{m^3}-$ air density; $=0\mathrm{.}25-$ turbine efficiency $($dimensionless$)$; $A=*r^2-$ area swept by turbine blades, $r=30m-$ length of turbine blades.

The turbine is turned on when the wind velocity exceeds the "cut$-$in$"$ value velCutln $=5\mathrm{.}4\frac{m}{s}.$ The turbine

Complete the following steps:

Create variables with values of all turbine parameters. Using a random number generator, create a row array velWind containing simulated daily wind velocity values. The values have to be normally distributed random numbers with a desired average of $15\frac{m}{s}$ and a standard deviation of $6c\frac{m}{s}.$ The number of elements in velWind has to be a random integer number between $60$ and $80.$ Use $rng(1)$ function to ensue repeatability of random numbers.

Create an array days with day numbers from $1$ to the last index of velWind. Using logical array indexing $($no loops$),$ create arrays velLow, velHigh, and velGood with velocity values from the array velWind within in the following ranges:Create an array daysGood containing day numbers when power was generated.Find the number of elements in each of the $3$ velocity arrays. Calculate percentages of respective numbers of days over the observation period$\mathrm{.}3.$ Calculate power generated by the turbine using local function TurbinePower and the formula given above for power$-$generating days. The function should have input arguments velGood, r$,$rou,mu and output argument pwrWind. Convert the array pwrWind from Watts to MegaWatts $($MW$)\mathrm{.}4.$ Find average and standard deviation of produced power $($in MW$)$ over all power$-$generating days using built$-$in MATLAB functions$\mathrm{.}5.$ Using array concatenation $($no loops$),$ create a $3-$colmn array dataOut, in which the $1^("$st $")$ column contains numbers of power$-$generating days, $2^("$nd $")$ and $3^("$rd $")$ columns contain corresponding wind velocity and power values. Use transposition to convert row arrays to column arrays$\mathrm{.}6.$ Print numbers of days and their percentages for days when power was produced and days without power. Print the average and the standard deviation power for power$-$generating days with $2$ and $1$ digits after the decimal point, respectively. Include parameter description and their units. Print the $3$column array dataOut with day numbers printed as integers, wind velocity and power values printed with $1$ and $3$ digits after the decimal point, respectively. Print column headings with parameter names and units.

Organize your script in Input, Calculations, and Output sections. Include cleaning commands; provide comments; suppress intermediate output. Use only those Matlab methods that were described in class.