I need parts A,B and C answered 5. A new private space company called Space Futu

Question

I need parts A,B and C answered

5. A new private space company called Space Futurama is testing out new rockets. Each new rocket has probability .75 of taking off successfully (independent across different rockets). (a) 1 point Find the probability that in the next 10 attempts, at least 7 ( 7) rockets take of successfully (b)1 point Let X be the number of rockets that take off successfully in the next 10 rockets. Find E(X) (just give the answer, no need to show work). (e) 1 point Find Var(X) Gust give the answer, no need to show work)

Explanation / Answer

P(success)=0.75

a) P(x>=7) = P(7)+P(8)+P(9)+P(10) =10C7*(0.75)^7*(0.25)^3 +10C8*(0.75)^8*(0.25)^2 +10C9*(0.75)^9*(0.25)^1+10C10*(0.75)^10*(0.25)^0 =0.7758

b) E(x)=n*p =10*0.75=7.5

c) Var(x) =n*p*(1-p)= 10*0.75*0.25 =1.875

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