6. In the Pirates of the Aegean video game, you may have to investigate 0, 1, 2, 3, 4, or 5 grottoes without success before you finally locate a treasure chest. You conclude that the probability you will have to investigate at mostxgrottoes without success is , and F(5) = 1. (Remember that is the number of permutations(ordered lists withoutreplacement) of kitems from npossibilities.)a) What is the probability you will have to investigate exactly 3 grottoes without success?b) What is the expected numberE(X) of grottoes you will investigate without success?c) What is the variance Var(X) of the number of grottoes you will investigate without success?

a) probability of investigating exactly 3 grottoes = 1/6

b) E(x) = 2.5

c) Var(x) = 2.918

Step-by-step explanation:

Since there are 6 cases in the distribution, the number of elements in the sample space is 6

a) probability of investigating exactly 3 grottoes = 1/6

b) Expected value E(x) = ∈(xP(x))

E(x) = (0*1/6) + (1*1/6) + (2*1/6) + (3*1/6) + (4*1/6) + (5*1/6)

E(x) = 2.5

c) variance of x, Var(x) = ∈ [(E(x) - x)² * P(x)]

Var(x) = [(2.5-0)²*1/6] +  [(2.5-1)²*1/6] + [(2.5-2)²*1/6] +  [(2.5-3)²*1/6] +  [(2.5-4)²*1/6] +  [(2.5-5)²*1/6]

Var(x) = 1.042 + 0.375 + 0.042 + 0.042 + 0.375 + 1.042

Var(x) = 2.918

1gm = 1000mg so 0.1gm = 1000mg

first, convert the weight to kg

160lb * 1kg/2.2lb = 72.7kg

next, the dose

72.7kg * 100mg/kg = 7270mg

step-by-step explanation:

what grade level is this? need to know so i can look in my old textbooks!