On the midnight shift, the number of patients with head trauma in an emergency room has the probability distribution shown below. х P(x) 0 .09 1 .32 2 3 .27 .17 4 .11 5 .04 Total 1.00 (a) Calculate the mean and standard deviation. (Round your mean value to 2 decimal places and standard deviation to 3 decimal places.) Mean Standard deviation LI​

2.01 ; 1.918

Explanation:

Given the data:

X : 0 __ 1 ___ 2 ___ 3 4 5

P(x) : 0.09 _ 0.32 _0.27_0.17___0.11 __ 0.04

The mean, E(x) :

Σ(X * p(x))

= (0*0.09)+(1*0.32)+(2*0.27)+(3*0.17)+(4*0.11)+(5*0.04) = 2.01

Standard deviation = sqrt(variance)

Variance = Var(x)

Var(X) = Σx²*p(x) - E(x)

Σ[(0^2 * 0.09) + (1^2 * 0.32) + (2^2 * 0.27) + (3^2 * 0.17) + (4^2 * 0.11) + (5^2 * 0.04)] - 2.01

= 5.69 - 2.01

= 3.68

SD(x) =sqrt(3.68)

SD(x) = 1.918

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