Question

4. Suppose that 75% of the students in a large class know how to answer a particular test question correctly. You take a random sample of n = 5 student exams from the class. (a) What is the probability that none of the 5 students answered the test question correctly? (b) If the instructor gives no partial credit. 4 points for a correct answer and 0 points for an incorrect answer, i. What are the mean and standard deviation of the average number of points scored by the five students? ii. What are the mean and standard deviation of the total number of points scored by the five students?

Answer 1

a)P(none of the 5 answered correctly) =(1-0.75)⁵ =0.00098

b)

for one student:

x	f(x)	xP(x)	x2P(x)
0	0.2500	0.0000	0.0000
4	0.7500	3.0000	12.0000
	total	3.0000	12.0000
	E(x) =μ=	ΣxP(x) =	3.0000
	E(x2) =	Σx2P(x) =	12.0000
	Var(x)=σ2 =	E(x2)-(E(x))2=	3.0000

i)

mean of the average points μx=3

and standard deviation of the average =√(3/5) =0.7746

ii)

mean of the total points μT=3*5 =15

and standard deviation of the total =√(3*5) =3.8730