Consider a sampling distribution with p equals 0.12 and samples of size n each. using the appropriate formulas, find the mean and the standard deviation of the sampling distribution of the sample proportion.
(a) for a random sample of size n equals 5000.
(b) for a random sample of size n equals 1000.
(c) for a random sample of size n equals 500.

Consider a sampling distribution with p equals 0.12 and samples of size n each.

Then, formula for mean = p

Formula for standard deviation=

(a) For a random sample of size n equals 5000.

Mean = 0.12

Standard deviation=

(b) For a random sample of size n equals 1000.

Mean = 0.12

Standard deviation=

(c) For a random sample of size n equals 500.

Mean = 0.12

Standard deviation=

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this