Question

1.The following probability distribution lists the probability of getting a certain number of questions correct on a five question True/False quiz.

Five-question true/false quiz

( x = number correct)

x P(x)

0 0.03125

1 0.15625

2 0.3125

3 0.3125

4 0.15625

5 0.03125

1A. What is the mean of the probability distribution?

1B. What is the standard deviation?

1C. What is the probability of getting more than 3 questions correct?

2.

2A. The probability that a student passes a certain math exam in 0.7. If the exam is given to 15 students, find the probability that at least 12 of them pass? Hint: This is binomial calculator

2B.On a typical day a credit union opens 5 new accounts. Find the probability that the credit union opens exactly 6 accounts in the next two days. Hint: Use Poisson calculator

Answer 1

solution:

X	p(X)p(X)	X*p(X)	X2(p(X))
0	0.03125	0*0.03125=0	02 * 0.03125 = 0
1	0.15625	1*0.15625=0.15625	12 * 0.15625 = 0.15625
2	0.3125	2*0.3125=0.625	22 * 0.3125 = 1.25
3	0.3125	3*0.3125=0.9375	32 * 0.3125 = 2.8125
4	0.15625	4*0.15625=0.625	42 * 0.15625 = 2.5
5	0.03125	5*0.03125=0.15625	52 * 0.03125 = 0.78125

0 + 0.15625 + 0.625 + 0.9375 + 0.625 + 0.15625 = 2.5

E(X2) = 0 + 0.15625 + 1.25+ 2.8125 + 2.5 + 0.78125 = 7.5

probability of getting more than 3 questions = p(X=4) + P(X= 5) = 0.15625 + 0.03125 = 0.1875

solution 2A)

p= 0.7, n= 15

using bionomial formula

2B) average accounts open in a given day = 5

so, accounts open in the two days = 2 * 5 = 10

so