Bridges Name __________________________Math 115b Team # _____SOME PROJECT 2 REVIEW QUESTIONS1. Write the solution to each of these integrals in the blank. Then briefly explain how you determined your answer.(a)¿¿¿¿¿(x−5)2(16)dx=¿¿∫28¿(b)¿¿¿¿¿x(16)dx=¿¿∫28¿(c)¿¿¿¿¿∫−∞∞1√2 π∙ e−0.5 z2dz=¿¿(d)¿¿¿¿¿(x−7)2(17)e−x /7dx=¿¿∫0∞¿2. Let X be the number of days that a heart transplant recipientin the U.S. stays in the hospital after his transplant. An insurance excective wants to estimate the mean and thestandard deviation. To do this, she takes a random sampleof 4 transplant recipients. The number of days for whichthese people were hospitalized are: 8, 9, 10, 9.Find the mean and the standard deviation of this sample.3. Let X be a random variable with a mean of 72 and astandard deviation of 7. Let x(bar) be the sample mean forrandom samples of size n = 20. Compute the expected value,the variance and the standard deviation of x(bar), given the4. From the list below, choose the best name or the best expression of what eachformula represents. fZ( z )=1√2⋅π⋅e−0. 5⋅z2V ( X )=n⋅p⋅(1− p )fX( x )={0 if x<01α⋅e−x / αif x≥0__________________________________________________________________________________E( X )=∫−∞∞x⋅fX( x )dxFX( x )={0 if x<ax−ab−aif a≤x≤b1 if x>bE( X )=n⋅p__________________________________________________________________________________2E( X )=∑all xx⋅fX( x )V ( X )=(b−a )212fX( x )={0 if x<a1b−aif a≤x ≤b0 if x>b__________________________________________________________________________________V ( X )=α2V ( X )=∑all x(x−μX)2⋅fX( x )V ( X )=∫−∞∞(x−μX)2⋅fX( x )d x__________________________________________________________________________________E( X )=a+b2FX( x )={0 if x<01−e−x /αif x≥0E( X )=α__________________________________________________________________________________Choose your answers from this set. Some of these expressions may be used more than once and some may not be used at all: random variable = ran var; expected value = exp val; st dev = standard deviationcdf – binomial ran var cdf – uniform ran varpmf – binomial ran var pdf – uniform ran varexp val – binomial ran var exp val – uniform ran varvariance – binomial ran var variance – uniform ran varcdf – normal ran var exp val – any finite ran varpdf – normal ran var variance – any finite ran varcdf – standard normal ran var exp val – any continuous ran varpdf – standard normal ran var variance – any continuous ran varcdf – exponential ran var relationship between variance and st devpdf – exponential ran var exp val or mean of a sampleexp val – exponential ran var variance of a samplevariance – exponential ran var standardizationrelationship between the variance of the mean of a sample and the variance of the entire random variable5. Calculate the 90% Confidence Interval.You have been working at the corporate headquarters of Supreme Sports, Inc for two years. Having been the leader of the team that has created several innovative commodities in the area of skiing, you believe that you deserve a raise, especially since these commodities have sold quite well in the market. Your salary is currently $96,500. You take a sample of 50 other team leaders from several other companies whose performance has been similar to yours and who have worked for their respective companies for two years. The mean of this sample is $98,900 and the standard deviation is $23,700.(a) Given that P(−1.645 ≤ Z ≤ 1.645)=0.90, calculate to the nearest 2 decimal places the 90% confidence interval for this sample. SHOW ALL WORK.36. Standardization of a Random VariableLet W be an exponential random variable with ∝=5.3. (a) Find the standardization S of W.(b) Find −0.7 ≤ S ≤
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