Statistics and Probability Answers

Historically the results of a final exam given by a particular teacher have a mean of 65.3% with a standard deviation of 8.5.
Calculate the probability of a student getting a mark between
i) 75 and 85
ii) 79 and 81
iii) 79.9 and 80.1

A beach resort buy a policy to insure against loss of revenues due to major storms in the
summer. The policy pays a total of $ 50,000 if there is only one major storms during
the summer, a total of $ 100,000 if there are two major storms, and a total payment
of $ 200,000 if there are more than two major storms. The number of major storms in
one summer is modeled by a Poisson distribution with mean of 0.5 per summer. Find
(a) Find the expected premium for this policy during one summer.
(b) the standard deviation of the cost of providing this insurance for one summer.

The loss due to an earthquake in a commercial building is modelled by a random variable X with density function f(x) =0.005(20−x), for 0 < x < 20 0, elsewhere Given that the fire loss exceeds 10, what is the probability that it exceeds 18.

An archer shoots arrows at a circular target where the central portion of the target inside is called the bull. The archer hits the bull with probability 1/32. Assume that the archer shoots 96 arrows at the target, and that all shoots are independent (a) Find the probability mass function of the number of bulls that the archer hits. (b) Give an approximation for the probability of the archer hitting no more than one bull.

Q#1: Let X denote the number of times a certain numerical control machine will malfunction: 1,
2, or 3 times on any given day. Let Y denote the number of times a technician is called on an
emergency call. Their joint probability distribution is given as: [0.5+0.5+1+1+1+1]
f x y ( , )
x
1 2 3
y
1 0.05 0.05 0.10
2 0.05 0.10 0.35
3 0.00 0.20 0.10
a) Evaluate the marginal distribution of X;
b) Evaluate the marginal distribution of Y;
c) Find the mean of X and Y;
d) Find the variance of X and Y;
e) Find the correlation coefficient between X and Y;
f) Interpret the result find in part (e).

Suppose that 3% of computer chips produced by a certain machine are defective. The chips are put into packages of 20 chips for distribution to retailers. What is the probability that a randomly selected package of chips will contain at least 2 defective chips.

A recent study shows that the annual cost of maintaining a building in Accra averages
200 Cedis with a variance of 260 Cedis. If a tax of 30% is introduced on all items
associated with the maintenance of building i.e. everything is made 30% more expensive.
Calculate the standard deviation of the annual cost of maintaining a building in Accra

[img]https://upload.cc/i1/2020/05/09/rMhjRP.jpg[/img]

A package of 6 fuses are tested where the probability an individual fuse is defective is
0.05. (That is, 5% of all fuses manufactured are defective).
(a) What is the probability one fuse will be defective?
(b) What is the probability at least one fuse will be defective?
(c) What is the probability that more than one fuse will be defective, given that at
least one is defective?

An archer shoots arrows at a circular target where the central portion of the target
inside is called the bull. The archer hits the bull with probability 1/32. Assume that
the archer shoots 96 arrows at the target, and that all shoots are independent
(a) Find the probability mass function of the number of bulls that the archer hits.
(b) Give an approximation for the probability of the archer hitting no more than one
bull.