Question

1) The daily demand, D, of sodas in the break room is:

D	0	1	2	3
P=(D=d)	0.1	0.2	0.4	0.3

i) Find the probability that the demand is at most 2.
ii) Compute the average demand of sodas.
iii) Compute SD of daily demand of sodas.

2) From experience you know that 83% of the desks in the schools have gum stuck
beneath them. In a random sample of 14 desks.
a) Compute the probability that all of them have gum underneath.
b) Compute the probability that 10 or less desks have gum.
c) What is the probability that more than 10 have gum?
d) What is the expected number of desks in the sample have gum?
e) What is the SD of the number of desks with gum?

3) The number of customers, X, arriving in a ATM in the afternoon can be modeled
using a Poisson distribution with mean 6.5.
a) Compute P(X<3).
b) Compute P(X>4).
c) SD of X.

Answer 1

1)

i) The probability that the demand is at most 2 is P(d <=2) = 0.1 + 0.2+ 0.4 = 0.7

ii) From the given data

X	P(X=x)	xP(X=x)	X^2P(X=x)
0	0.1	0	0
1	0.2	0.2	0.2
2	0.4	0.8	1.6
3	0.3	0.9	2.7
Total:	1	1.9	4.5

2) From experience you know that 83% of the desks in the schools have gum stuck beneath them. In a random sample of 14 desks.

i.e. n = 14 and p = 0.83

a) Compute the probability that all of them have gum underneath.

P(X=14) = 0.83^14 = 0.0736

b) Compute the probability that 10 or less desks have gum.

c) What is the probability that more than 10 have gum?

P(X>10) = 1 - P(X<=10) = 1 - 0.2038 = 0.7962

d) What is the expected number of desks in the sample have gum?

E(X) = np = 14*0.83 = 11.62

e) What is the SD of the number of desks with gum?

SD = Sqrt(npq) = sqrt(14*0.83*0.17) = 1.4055

3) The number of customers, X, arriving in a ATM in the afternoon can be modeled
using a Poisson distribution with mean 6.5.

a) Compute P(X<3).

b) Compute P(X>4).

c) SD of X.

SD = Sqrt(Lamda) = Sqrt(6.5) = 2.5495