This is due today, and I have no idea what I'm doing, please help if you know anything.

Binomial distribution formula: P(x) = (n  k) p^k * (1 - p)^n - k

a) Probability that four parts are defective = 0.01374

P(4 defective) = (25 4) (0.04)^4 * (0.96)^21

P(4 defective) = 0.01374

b) Probability that at least one part is defective = 0.6396

Find the probability that 0 parts are defective and subtract that probability from 1.

P(0 defective) = (25 0) (0.04)^0 * (0.96)^25

P(0 defective) = 0.3604

1 - 0.3604 = 0.6396

c) Probability that 25 parts are defective = approximately 0

P(25 defective) = (25 25) (0.04)^25 * (0.96)^0

P(25 defective) = approximately 0

d) Probability that at most 1 part is defective = 0.7358

Find the probability that 0 and 1 parts are defective and add them together.

P(0 defective) = 0.3604 (from above)

P(1 defective) = (25 1) (0.04)^1 * (0.96)^24

P(1 defective) = 0.3754

P(at most 1 defective) = 0.3604 + 0.3754 = 0.7358

e) Mean = 1 | Standard Deviation = 0.9798

mean = n * p

mean = 25 * 0.04 = 1

stdev =

stdev = = 0.9798

Hope this helps!! :)

2 x^2 -3x+p

sum of roots = 3/2

let other root be x

3+ x = 3/2

x= 3/2 - 3 = -3/2

product of roots = p/2

3× -3/2 = p/2

-9 = p

⭐⭐

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