Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. This instructor is about to give two exams, one to a class of size 25 and the other to a class of size 64. Required:
a. Approximate the probability that the average test score in the class of size 25 exceeds 80.
b. Repeat part (a) for the class of size 64.
c. Approximate the probability that the average test score in the larger class exceeds that of the other class by over 2.2 points.

a) Hence the probability that the average test score in the class of size 25 exceeds 80.

P ( X > 74) = 0.9838

P ( Z > 2.14) = 0.0162

b) Hence the probability that the average test score for the class of size 64

P ( X > 74) = 0.9838

P ( Z > 2.14) = 0.0003

c) Probability of the difference exceeding 2.2 = 0.9936

P (Z < 2.49) = 0.0064

Step-by-step explanation:

Let's assume a normal distribution.

Now,

a) For a class of 25

b)

Similarly:

For the class of 64

c) Probability of the difference exceeding 2.2

P (Z < 2.49)

= 1 - 0.9936

= 0.0064

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

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.