Assessment OF: Statistics of One Variable Assignment
Wind speed data has been collected from two different weather stations over the course of fifty days of stormy weather.
Stormy Weather on the Baltic Sea
Raw data is collected from Rockall- the wind speeds, measured in km/h on the fifty days in the study are recorded, in ascending order, in the table below:
Find the mean, mode and median wind speeds, and comment on your findings.
Use Excel to find the standard deviation of the wind speeds, and explain its relevence.
Find the upper and lower quartiles of the data, and use them to draw a box and whisker diagram of the wind speeds. Use a scale that goes up to 130 km/h so that you can fit the second data set on it also.
This is the BBC: Announcer Frank Phillips pictured broadcasting in the early Fifties.
The wind speed data from North Utsire is given as grouped data:
|Wind speed (w km/h)||Frequency|
|30 ≤ w < 40
|40 ≤ w < 50
|50 ≤ w < 60
|60 ≤ w < 70
|70 ≤ w < 80
|80 ≤ w < 100
|100 ≤ w < 130
Find the mean wind speed.
Draw a histogram to represent the distribution of wind speeds.
Create a cumulative frequency table, and from it, draw a cumulative frequency curve. Use the curve to find the median and upper and lower quartiles.
What do the mean, median and quartiles tell you about the distribution of wind speeds in North Utsire?
Use the median and quartiles to draw a box and whisker diagram on the same scale as the one for Rockall.
Analysis and Comparison
Describe what the various calculations and graphical representations have told you about the wind speeds in North Utsire and Rockall. Draw comparisons between the two weather stations.
Assessment OF: Statistics of Two Variables Assignment
- Sketch a scatter plot that could represent data from each of the following. Label the axes to indicate the independent and dependent variable.
- people’s ages (starting at 20) and their reaction times
- size of a house and its price
- exposure to sunlight and the risk of heart attacks
- size of vocabulary and age (birth to 25 years old)
- oven temperature and the cooking time for a turkey
A study was done with a group of university students to determine if there was a correlation between the amounts of sleep they got and their academic performance. The following table lists some data from the study.
|Hours of Sleep
|Hours of Sleep
- Make a scatter plot of the data.
- Using a spreadsheet, determine the PPMCC.
- What would you conclude about the relationship between the two variables?
- A recent study found that people who illegally download music spend more on music than those who don't. These findings are often cited as evidence that piracy does not harm music sales, and can even enhance them.
- Read the article here : http://www.escapistmagazine.com/news/view/120147-Survey-Indicates-Music-Pirates-Are-Biggest-Music-Buyers
Explain why the commonly reached conclusion to these findings may
not be correct.
- Give an example of each of the following types of causal relationships, fully explaining your suggestion:
- common-cause factor
- accidental relationship
- reverse cause and effect relationship.
Assessment OF Learning: Combinatorics Assignment
- Mr Baker is ordering a pizza. He has four sizes to choose from, three types of crust, four sauces, five types of cheese, and six optional toppings.
How many different pizzas could he create?
Give a full explanation for your answer.
- Idi is creating a password for a website that has some strict requirements. The password must be 8 characters. Numbers and letters may be used, but may not be repeated.
How many are possible if the following restrictions are enforced;
- How many diffferent passwords are possible?
- The password must feature both numbers and letters?
- The password must start with a letter?
- The password must start with a letter and end with a number?
- Marissa is doing a Tarot reading in which she must pick 6 cards from a deck of 72. The order of their selection is not important.
- How many different readings are possible?
- Marissa does not want to see the Fool card. How many of the possible readings do not feature the Fool?
- A teacher organizing a field trip finds that 50 students have signed up. However, the bus has only 47 seats, so a few students will have to travel by car. The teacher and one other supervisor must go on the bus. Explain two different methods for using combinations to find how each teacher can choose which students go on the bus. Show that both methods produce the same answer.
- A committee of 5 people is to be chosen from a group of 8 women and 10 men.
How many are possible if the following restrictions are enforced;
- How many diffferent committees are possible?
- The committee must feature both men and women?
- The committee must feature 3 women and two men?
- The committee must have more women than men?
A circle has 12 equally spaced marks around its outside:
Triangles can be drawn by joining up three of the marks:
- How many different triangles can be drawn?
- If we only count non-congruent triangles (ie the three below, and all others congruent to them, count as the same triangle), how many different triangles are there?
- Simplify each expression and write it without using factorial notation.
||(n + 4)!
||(n + 2)!
||(n − r + 1)!
||(n − r − 2)!
- We have looked at situations in which we need to determine the number of possible routes between two places. We can look at the situation below as 9 steps, six of which must be East and three of which must be South.
|This gives us
|| = 84 possible routes
|| is equivalent to 9C3 (or 9C6)
- Explain clearly why you could solve this question using combinations, and why this is equivalent to considering permutations with repeated items.
- How many different ways are there of getting from the green dot to the red dot, moving only right or down? Explain your answer in terms of both permutations and combinations.
- How many ways are there for a spider to crawl from the green point to the red on the 3-dimensional frame below, given that he wants to crawl the shortest possible distance?
I have a number of dogs and monkeys living with me. If I decide to take out for a walk a monkey AND a dog, I find I have fewer options than if I decide to take out a monkey OR a dog.
A monkey AND a dog
What can you say about the numbers of monkeys and dogs I live with?
Fully explain your answer.
- Investigate a lottery competition somewhere in the world. Explain how the lottery works, and what needs to happen for someone to win the jackpot, and at least one of the minor prizes.
Calculate the probability of winning each of the prizes you described, giving a full explanation of your work.
Consider the cost of playing. Do you think the prizes on offer are fair? If not, why not, and why do you think people continue to play?
Assessment OF: Probability Assignment
Toronto and Vancouver are playing a series in which alternate games are played in each city. The first game is played in Toronto, where the home team have a 70% chance of winning. Vancouver have a 60% chance of winning when they play at home.Given that ties are not possible;
- Create a tree diagram to show all possible outcomes.
- What is the probability that Toronto wins the series in four games?
- What is the probability that the series goes to a fifth game?
- We have looked in detail at three probability distributions; binomial, geometric and hypergeometric. For each one,
- Explain the conditions in which we would use it.
- Justify the formula used
- Give an example of a situation in which it could be used.
Kazuki is playing a Scratch-and-Win competition in which the chance of winning a pet albatross is 1/15.
He decides to keep playing until he wins.
Showing your calculations, find the probability he
- Create a probability distribution table and graph of the number of attempts it takes to win, from 1 up to 20.
- Wins an albatross on his eighth attempt.
- Wins an albatros before his tenth attempt.
- Still hasn't won an albatross after his 20th attempt.
- ShiQi is taking a multiple choice quiz. There are 20 questions, and four possible answers for each question, but she hasn't revised, and she guesses all the answers.
Showing your calculations, find the probability she;
- Create a probability distribution table and graph of the number of correct answers she gets.
- Scores 8 out of 20.
- Passes the test (ie scores 10 or above).
Scientists are studying a group of 40 polar bears. 14 of them have been tagged. They take a sample of 6 bears.
- Create a probability distribution table and graph of the number of tagged polar bears in the sample.
- Showing your calculations, find the probability the sample contains 2 tagged bears.
- Explain how an unknown population might be estimated through the process of tagging animals.
Air Canada's planes begin flying out of Toronto at 7am, and leave every 30 minutes. The probability of a flight being late is 15%, but once a flight is delayed, all subsequent flights are also late.
Showing your calculations, find the probability;
- The first late flight is the fourth departure.
- The 11am flight takes off on time.
- The flight scheduled for 1:30pm is delayed.
- A company manufacturing laptops believes that 5% of their computers are faulty. They take a sample of 30 computers. Showing your calculations, find the probability;
- Two of the laptops are faulty.
- More than two of the laptops are faulty.
- Think back to the Thumb-Tack Roulette game. How much of an advantage is it to go second? Explain your answer carefully and clearly.
- Look at the sketches of continuous probability distributions below.
For each sketch, give an example of a situation which might give rise to such a probability distribution, fully explaining your reasoning.
- In many situations, the normal distribution can be used to approximate the binomial distribution.
- Explain the conditions in which this can be done, and explain why we might want to take advantage of this property.
- Give an example of a situation in which we could do this.
- Give an example of a situation in which we would not be able to make this approximation and explain why.
A species of alien has a mean height of 23 cm and a standard deviation of 3.6 cm.
What is the probability that an alien chosen at random has a height of more than 20cm?
- Researchers have observed that regular smokers have an average lifespan that is normally distributed and is 68 years with a standard deviation of 10 years. What percent of smokers will live beyond age 76?
A very aptly named brand
- The life span of a particular species of turtle are normally distributed with a mean of 180 years and a standard deviation of 40 years. What is the probability that one of these turtles will live more than a century?
- A second species of alien has a mean height of 71 cm and a standard deviation of 5.3 cm. An alientologist discovers that 30% of them bump their heads getting into their spaceship. What is the height of the spaceship door?
- In Bayfield, 65% of residents read the Bayfield Breeze, a local online blog. Dennis wants to know what people think of the blog, so he stops 40 people on the street to ask them if they read it.
- Verify that the normal distribution can be used to approximate this situation.
- What is the mean and standard deviation of the number of people he finds that read the Breeze?
- What is the probability that at least 25 of the people he asks read the blog?
Yuen Zhi is running a ring toss event at a school fair.
There is a 15% chance that each attempt wins a prize. She has 45 prizes and believes 250 people attempt the event.
She is worried she won't have enough prizes. Can you reassure her she will probably be ok?
- We have been using the normal distribution to approximate situations that are in fact binomial events.
- Demonstrate how accurate the approximation is by using both approaches to find the probability of the same event.
- Describe the conditions under which the normal would give a less accurate approximation.
- Explain a situation in which the criteria for using the approximation would be met, ie. np ≥ 5 and n(1 − p) ≥ 5, and yet you would decide not to use the normal distribution.
|Due By (Pacific Time)
||05/28/2013 12:00 pm