A χ2 goodness-of-fit test is performed on a random sample of a bag of 30 Skittles® to determine whether the proportion of each flavor (strawberry, orange, lemon, lime, and grape) is equal to the claimed amount (20% of each flavor). The χ2 statistic is determined to be 10.20. What is the p-value for this test? (4 points) A 0.001 < p < 0.005

B 0.02 < p < 0.025

C 0.025 < p < 0.05

D 0.10 < p < 0.15

E 0.05 < p < 0.10

C. 0.025 < p < 0.05

Step-by-step explanation:

The goodness-of-fit test parameters are presented here as follows;

The number of Skittles in the bag = 30 Skittles

The different flavors in the bag of Skittles = Strawberry, orange, lemon, lime, and grape

The number of different flavors, n = 5 flavors

The statistic = 10.20

Therefore, the degrees of freedom, d.f. = n - 1 = 5 - 1 = 4

Using the chi-square () distribution table,  we have;

The probability at 4 degrees of freedom for a statistic of 10.20 is between 0.025 and 0.05

Therefore, we get;

The probability (P > 10.20) = 0.025 < p < 0.05.

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