Question

11. The 4077th Mobile Army Surgical Hospital hospital is considering the purchase of a helicopter to transport critical patients. The relative frequency of X, the number of times a helicopter is used to transport critical patients each month, is determined from a similarly-sized army hospital as given by the probability distribution. Number of Helicopter Transports X 01 2 3 4 5 P(X) 0.15 0.20 0.34 0.19 0.06 0.05 6 0.01 (a) Verify that this is a valid probability distribution. (b) Find the mean number of times the helicopter is used to transport critical patients each month. Use proper notations, show work, don't forget units (c) Find the variance and standard deviation of the number of times the helicopter is used to transport critical Use proper notations, show work, don't forget units (0) patients probability that a helicopter will not be used at all to transport patients. Use probability notations (e) Find the probability that a helicopter will be used at least once to transport critical patients Use probability notations
I need help with question 11 part A,B, C, D, and E

Answer 1

a)

for this to be valid:

$\sum$P(x) =P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6) must be1

$\sum$P(x) =P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+P(X=5)+P(X=6)=0.15+0.2+0.34+0.19+0.06+0.05+0.01

=1

since all individual sample point probabilities are between 0 and 1 and sum of probability of all sample point is 1, this is a valid probability distribution

b)

E(X)=$\sum$xP(x) =0*0.15+1*0.2+2*0.34+3*0.19+4*0.06+5*0.05+6*0.01=2

c)

E(X²)=$\sum$x²P(x) =0^2*0.15+1^2*0.2+2^2*0.34+3^2*0.19+4^2*0.06+5^2*0.05+6^2*0.01=5.84

Var(x)=σ2 =

E(x2)-(E(x))2=

1.8400

std deviation=

σ= √σ2 =

1.3565

d)

P(X=0) =0.15

e)\

P(X>=1) =1-P(X=0)=1-0.15 =0.85