When parking a car in a downtown parking lot, drivers pay according to the number of hours or fraction thereof. The probability distribution of the number of hours cars are parked has been estimated as followsA. Mean=B. Standard Deviation=The cost of parking is 5 dollars per hour. Calculate the mean and standard deviation of the amount of revenue each car generates. A. Mean=B. Standard DeviationX 1 2 3 4 5 6 7 8P(X) 0.229 0.113 0.114 0.076 0.052 0.027 0.031 0.358

u = 4.604 , s = 2.903

u' = 23.025 , s' = 6.49

Step-by-step explanation:

Solution:

- We will use the distribution to calculate mean and standard deviation of random variable X.

- Mean = u = E ( X ) = Sum ( X*p(x) )

 u = 1*0.229 + 2*0.113 + 3*0.114 + 4*0.076 + 5*0.052 + 6*0.027 + 7*0.031 + 8*0.358.

 u = 4.604

- Standard deviation s = sqrt ( Var ( X ) = sqrt ( E ( X^2) + [E(X)]^2

 s = sqrt [ 1*0.229 + 4*0.113 + 9*0.114 + 16*0.076 + 25*0.052 + 36*0.027 + 49*0.031 + 64*0.358 - 4.604^2 ]

s = sqrt ( 8.429184 )

s = 2.903          

- We will use properties of E ( X ) and Var ( X ) as follows:

- Mean = u' = E (Rate*X) = Rate*E(X) = $5*u =

               u' = $5*4.605

               u' = 23.025

- standard deviation = s' = sqrt (Var (Rate*X) ) = sqrt(Rate)*sqrt(Var(X)) = sqrt($5)*s =

               s' = sqrt($5)*2.903

               u' = 6.49

for the first question it would be the second answer for the second question it would be the third answer and for the third question it would be the first answer

step-by-step explanation:

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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