# Poisson & Normal Probabilities

5.1 In a certain state, an appeals court consists of seven judges. For a routine case, three judges are chosen at random as a panel to hear a case and render a decision. How many distinct panels can be formed?

5.26 Logging trucks have a particular problem with tire failures due to blowouts, cuts, and large punctures; these trucks are driven fast over very rough, temporary roads. Assume that such failures occur according to a Poisson distribution at a mean rate of 4.0 per 10,000 miles.

a. If a truck drives 1000 miles in a given week, what is the probability that it does not have any tire failures?

b. What is the probability that it has at least two failures?

c. What is the expected value and standard deviation of the number of tire failures per 1000 miles driven?

5.35 A financial analyst states that the (subjective probability) price of Y of a long-term $1000 government bond one year later is normally distributed with expected value $980 and a standard deviation $40.

a. Find P(Y â?¥ 1000).

b. Find P(Y â?¤ 940).

c. Find P(960 â?¤ Y â?¤ 1060)

https://brainmass.com/statistics/probability/poisson-normal-probabilities-328542

#### Solution Summary

The solution provides step by step method for the calculation of probability using the Z score and Poisson distribution. Formula for the calculation and Interpretations of the results are also included.

Statistics: Contingecy table, probability distribution, portfolio expected return, Poisson distribution, normal distribution, standard deviation

See attached file for format and formulas.

Q4: 4 (+) Given the following contingency table:

B B'

A 10 30

A' 25 35

Find the following:

a) A | B

b) A' | B'

c) A | B'

Q4: 5 The manager of a large computer network has developed the following probability distribution of the number of interruptions per day:

Interruptions (X) P(X)

0 0.32

1 0.35

2 0.18

3 0.08

4 0.04

5 0.02

6 0.01

a. Compute the expected number of interruptions per day

Q4: 5 (+) Two investments, X and Y, have the following characteristics:

E(X) = $50, E(Y) = $100, s2X = $9,000, s 2y = $15,000, and s 2XY = $7,500.

If the weight of portfolio assets assigned to investment X is 0.4, compute the

a. portfolio expected return

s2x $9,000

s2y $15,000

s2xy $7,500

E(X) $50

E(Y) $100

w(x) 0.4

b. portfolio risk

Q4: 5 (+) Assume a Poisson distribution.

a. If lamda = 2, find P( X >= 2 ) l = 2

X = 2

Q4: 6 Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1,

as in Table E.2), what is the probability that:

a. Z is less than 1.57

b. Z is greater than 1.84

c. Z is between 1.57 and 1.84

Q4: 6 (+) Given a normal distribution with mean = 100 and standard deviation = 10, what is

a. P( X > 75 ) ? m = 100

b. P( X < 70 ) ? s = 10