For the purposes of constructing modified boxplots, outliers are defined as data values that are above Q3 by an amount greater than 1.5xIQR or below Q1by an amount greater than 1.5xIQR, where IQR is the interquartile range. Using this definition of outliers, find the probability that when a value is randomly selected from a normal distribution, is it an outlier. The probability that a random selected value taken from a normal distribution is considered an outlier is 0.0070.

For this problem I know the answer is 0.0070. However I am unsure of how to solve the problem. I know I must subtract Q3-Q1 , but I’m unsure of how to find the values to represent these quartiles.

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