What is the probability that a random sample of 50 individuals shows an average annual income of at least $50,000? Select the parameters of the distribution to calculate the probability:

E(x), σx

Step-by-step explanation:

We have to x be their average annual income we need to find p ( x => 50000)

To find this probability we need  E(x), σx

For we find p ( x => 50000) we find the z value for 50000, ie the # of standart deviations that 50000 is away form   E(x)

z = (x  -  E(x)/σx)

now  p ( x => 50000) = p (z => (x  - E(x)/σx )

hence we can say that, to find p ( x => 50000) we need the parameters E(x), σx

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12