Search & Filtering
A data set lists the weightsβΒ (grams) of a type of coin. Those weights have a mean of 5.41478 g and a standard deviation of 0.06439 g. Identify the weights that are significantly low or significantly high.
a) How many three-digit numbers can be formed from the six digits 2, 3, 5, 6, 7 and 9?
b) How many are less than 500? [2]
c) How many are even? [2]
3.2 Simplify
(
be no more race, but if the race is a draw, they run another race. They run a maximum of three races.
Each time they race, the probability that Mboma wins is 0.45 and the probability that there is a draw is
0.08.
4.1.1 Draw the tree diagram that present all possible outcomes of this competition and their
probabilities [7]
4.1.2 Calculate the probability that Masilingi wins the competition. [4]
they are outside, the probability that Rex, Rover and Garfield will attack the postman are 30%, 40% and
15%, respectively. Only one is outside at time, with probabilities 10%, 20% and 70%, respectively.
If the postman is attacked, what is the probability that Rex was the culprit? [
A box of a dozen mechanical components contains 7 good components and 5 bad components.Β Mr. Mechanical Engineer is preparing machine design for his four projects.Β One component is required per machine. He randomly selects 4 components from the box.
a. What is the probability that the Mr. Mechanical Engineer got at most one bad component?
b. What is the probability that Mr. Mechanical Engineer will have to get components from the box again?
P(x,a)=a^x(1-a)^(1-x)0<a<1,x={0,1}
A Coca-Cola machine is made in such a way that it dispenses 500ml of coke per pet bottle drink. Suppose it is known that the amount of coke dispensed follows a normal distribution with mean 500 and variance 400.
a) You enter a spaza shop where you take a 500 ml bottle of coke from the fridge to drink at the premises. What is the probability that the bottle you select contain more than 550 ml of coke? (4)
b) Belowhowmanymillilitresdoyouget25%ofthedrinks? (5)
c) Suppose you further select, nine of the 500 ml bottles of coke from the fridge to bring your relatives at home. What is the probability that the all the nine bottles contain at least 4950 ml of coke? (5)
d) What is the probability that the mean contents of the selected nine bottles will be at least 440ml and at most 520 ml. (6)
e) Below what mean value do you find 25% of the sampled average content? (5)
a) Normal Distribution
b) Poisson Distribution
c) Chi-squared Distribution
d) Binomial Distribution
c) If ππ1, ππ2, ... , ππππ is a random sample from a distribution with mean ππ and variance ππ2, state whether the following expressions are statistics or not. Please explain your decision for each expression.
(2)
(2)
(2) (2) ( 2 )
βππππ ππ (i) ππ=1 ππ
(ii) 3
β ππππ = 1 ( ππ ππ β ππ ) 2
ππ2
(iii) ππ + ππ where ππ is a constant. (iv) Max(ππ1, ππ2, ππ3)
( v ) β ππππ = 1 ( ππ ππ β ππ ) 2
The joint probability density function of the random variables X and Y is f(x, y) = 2(x+2y) 7 , 0 < x < 1, 1 < y < 2, 0 , otherwise. Find the expected value of g(X, Y ) = X Y 3 + X2Y
