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In a school, 30 percent of the students do not travel by bus. From a sample
of 10 students find the probability that (a) at least 3 students travel by bus
(b) at most 4 students travel by bus (c) between 2 and 7 clients students
travel by bus (exclusive)
a research report that the average iq level of students in philiipines science highschool is 110 a sample of 20 students has a mean iq level of 106 woth a standard deviaton of 9
1. Consider rolling two dice once. Calculate the probability of the...
( a) rolling a sum of 5 or an even sum
(b) rolling a sum of 7 or 6
( c) rolling a sum of 10 or an odd sum
2. Six(6) woman , 4 men,3 boys and 7 girls enter a competition. They each have an equally likely chance of winning. What is the probability that the winner will be...
( a) female
( b) a child
( c) a man
3. A basket contains 12 black marbles ,14 red marbles and 12 green marbles. What is the probability of picking a black marble first and then a red marble with replacement
4. A bag contains 4 green,3 black and 6 orange cards. A card is drawn from the bag and kept, and then another card is drawn. Find the probability that
( a) both cards will be orange
( b) both cards will be black
( c) the first card will be orange and the second will be black
( d) neither will be orange.
According to a factory employer, the mean working time of workers in
the factory is 6 hours with a standard deviation of 0.5 hours
In a certain area, 50% of the household are using electricity as a source of energy, 30% are using parrafin and 20% are using coal. The users of electricity use 25% for cooking ,25% for lighting,20% for heating and 30% for small appliances. Coal is used for only cooking, and parraffin is used for cooking (50%) , heating (25%) and lighting (25%).
1. Summarise all the possible energy usage outcomes using a tree diagram and write the probability values on the branches.
2. What is the probability that a random choosen household will be using electricity for lighting?
The weights of normally distributed withe mean μ mg and standard deviation with σ mg. It is known that 25% of apples are heavier than 172 mg and 10% are lighter than 150 mg.
i) iilustrate the diagram to show the distribution of weghts based on the given information μ=150+1.2801σ
If x and g are two random variables,
there can be at most
(one / two / threelregression line(s)
A bag contains so many pink and yellow balls. A person can have 2 balls. Given that one of the balls is pink, what
is the probability that the other one is also pink?
(b) One hundred cars enter for a road-worthiness test which is in 2 parts mechanical and electrical. A car can only
pass if it passes both parts. Half the cars fail the electrical test and 62 pass the mechanical. 15 pass the electrical
and fail the mechanical test.
Find the probability that:
(i) A car chosen at random given that it has failed, failed the electrical test only
(ii) The Probability of fails on one test only will be
Measuring the height of a Yellow Meranti is very difficult because these trees grow to heights over 300 feet. In 2016, a group of Yellow Meranti in Sabah’s Danum Valley was announced as the tallest tropical trees in the world. People familiar with these trees understand that the height of a Yellow Meranti is related to other characteristics of the tree, including the diameter of the tree at the breast height of a person (in inches) and the thickness of the bark of the tree (in inches). The file YellowMeranti contains the height, diameter at breast height of a person, and bark thickness for a sample of 40 Yellow Meranti trees.
Discuss how you would ensure that an Ordinary Least Squares regression meet the BLUE requirement. (17marks)
