Math Answers

the annual salaries of employees in a large company are approximately normally distributed with mean of 162,000 and standard deviation of $100,000. what percent of people earn between $140,000 and $180,000

hi , I diagonalize hamiltonian H, then I found by chance , that this basis of eigenstates is also a basis of eigenstates of another operator let's call it "O" , which means that the Hamiltonian commute with that operator , before I diagonalizing in that basis , I have H (NxN matrix ) as will as (NxN) matrix for operator "O" , when I diagonalize the matrix of operator O I found that this operator have just two eigenvalues , two eigenstates as well (no matter what N ) , when I diagonalize H I found that it have N different eigenstates where part of them match the requirement of the first eigenstate of operator "O" and other part match the requirement of the second one , I want to understand mathematically how this match happens for example why would the ground state of the Hamiltonian match the requirement of the first eigenstate of operator O , . I wish that my question was clear , I am not a mathematician

X+y=1/9
Y+z=2/9
Z+x=5/9

Jo and David picked 92 quarts of berries at King’a Orchard. If David picked 6 more quarts than jo picked, how many quarts did Jo pick?

The cost of 5 boxes of envelopes and 5 packages of notebook paper is 25.95. Two boxes of envelopes and 6 packages of paper cost is 22.38. How much would one box of envelopes cost?

The probability that a person will die when he
or she contracts a virus infection is 0.001. Of the next
4000 people infected, what is the mean number who
will die?

The number of customers arriving per hour at a
certain automobile service facility is assumed to follow
a Poisson distribution with mean λ = 7.
(a) Compute the probability that more than 10 customers
will arrive in a 2-hour period.
(b) What is the mean number of arrivals during a
2-hour period?

Changes in airport procedures require considerable
planning. Arrival rates of aircraft are important
factors that must be taken into account. Suppose
small aircraft arrive at a certain airport, according to
a Poisson process, at the rate of 6 per hour. Thus, the
Poisson parameter for arrivals over a period of hours is
μ = 6t.
(a) What is the probability that exactly 4 small aircraft
arrive during a 1-hour period?
(b) What is the probability that at least 4 arrive during
a 1-hour period?
(c) If we define a working day as 12 hours, what is
the probability that at least 75 small aircraft arrive
during a working day?

An automobile manufacturer is concerned about
a fault in the braking mechanism of a particular model.
The fault can, on rare occasions, cause a catastrophe at
high speed. The distribution of the number of cars per
year that will experience the catastrophe is a Poisson
random variable with λ = 5.
(a) What is the probability that at most 3 cars per year
will experience a catastrophe?
(b) What is the probability that more than 1 car per
year will experience a catastrophe?

Find the mean and variance of the random variable
X in Exercise 5.61, representing the number of
persons among 10,000 who make an error in preparing
their income tax returns.