The number of chocolate chips in an 18-ounce bag of chips ahoy! chocolate chip cookies is approximately normally distributed with a mean of 1262 chops and standard deviation 118 chips according to a study by cadets of u. s. air force academy. (source: brad warner and jim rutledge, chance 12(1): 10-14, 1999)

(a) what is the probability that a randomly selected 18-ounce bag of chips ahoy! contains fewer than 1000 chocolate chips? (use 2-table)

(b) what is the probability that a randomly selected 18-ounce bag of chips ahoy! contains more than 1200 chocolate chips?

(c) what is the probability that a randomly selected 18-ounce bag of chips ahoy! contains between 1000 and 1400 chocolate chips, inclusive?

a) 0.013

b) 0.7

c) 0.866

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 1262

Standard Deviation, σ = 118

We are given that the distribution of number of chocolate chips is a bell shaped distribution that is a normal distribution.

Formula:

a) P(fewer than 1000 chocolate chips)

P(x < 1000)

Calculation the value from standard normal z table, we have,  

b) P(contains more than 1200 chocolate chips)

Calculating the value from the standard normal table we have,

c)P(contains between 1000 and 1400 chocolate chips)

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

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40