Questions and Answers of Descriptive Statistics

Paul and Gill decide to play a board game. The probability that Paul wins the game is 0.25 and the probability that Gill wins is 0.3. They decide to play three games. Given that the results of
The events A and B are such that P(A) = P(B) and P(AUB) - a Show that A and B are independent. b Represent these probabilities in a Venn diagram. e Find P(A|B).AppendixLO1
A computer game has three levels and one of the objectives of every level is to collect a diamond. The probability of a randomly chosen player collecting a diamond on the first level is the second
An online readers' club has 50 members. Glasses are worn by 15 members, 18 are left handed and 21 are female. There are four females who are left handed, three females who wear glasses and five
For the events / and K, PJUK) = 0.5, PK) = 0.2, P(JK') = 0.25. a Draw a Venn diagram to represent the events / and K and the sample space S. Find b PU), c P(K), e Determine whether or not J and K are
There are 15 coloured beads in a bag; seven beads are red, three are blue and five are green. Three beads are selected at random from the bag and not replaced. Find the probability that a the first
A survey of a group of students revealed that 85% have a mobile phone, 60% have an MP3 player and 5% have neither phone nor MP3 player. a Find the proportion of students who have both gadgets. b Draw
In a factory, machines A, B and C produce electronic components. Machine A produces 16% of the components, machine B produces 50% of the components and machine C produces the rest. Some of the
A garage sells three types of fuel; U95, U98 and diesel. In a survey of 200 motorists buying fuel at the garage, 80 are female and the rest are male. Of the 90 motorists buying 'U95' fuel, 50 were
A study was made of a group of 150 children to determine which of three cartoons they watch on television. The following results were obtained: 35 watch Toontime 54 watch Porky 62 watch Skellingtons
The members of a wine tasting club are married couples. For any married couple in the club, the probability that the husband is retired is 0.7 and the probability that the wife is retired 0.4. Given
The following scatter diagrams were drawn.a. Describe the type of correlation shown by each scatter diagram. b Interpret each correlation.AppendixLO1 Intelligence Height + x Price of a car x X Age x
Some research was done into the effectiveness of a weight reducing drug. Seven people recorded their weight loss and this was compared with the length of time for which they had been treated. A
Eight metal ingots were chosen at random and measurements were made of their breaking strength (x) and their hardness (y). The results are shown in the table below. x (tonne/cm) 5 7 7.4 6.8 5.4 7 6.6
For each of the following data sets plot a scatter diagram, and then describe the correlation. a x 1 2.4 3.6 2.2 4.3 3.3 4.0 0.6 y 6.0 9.0 15.8 7.1 18.6 12.1 15.0 3.7 b x 123 160 285 210 150 240 280
The table shows the armspan, in cm, and the height, in cm, of 10 adult men. Height x (cm) 155 160 173 192 181 178 199 166 158 173 Armspan y (cm) 147 159 165 180 a Draw a scatter diagram to represent
Eight students were asked to estimate the mass of a bag of sweets in grams. First they were asked to estimate the mass without touching the bag and then they were told to pick the bag up and estimate
Given x = 18.5 Ex = 36 n = 10 find the value of S AppendixLO1
Given y = 25.7 y2 140 n=5 find the value of S...AppendixLO1
Given x = 15 = 35 = 91 Exy 91 = n 5 find the value of Sy AppendixLO1
Given that S,, = 92, Syy 112 and Sy 100 find the value of the product moment correlation coefficient.AppendixLO1
Given the following summary data, = 367 = 270 Ex 33845 y 12976 Exy = 17135 calculate the product moment correlation coefficient (r) using the formula: Spy 11=6 AppendixLO1
The ages, a years, and heights, hcm, of seven members of a team were recorded. The data were summarised as follows: = a 115 Ea 1899 S571.4 72.1 a Find S b Find the value of the product moment
In research on the quality of bacon produced by different breeds of pig, data were obtained about the leanness () and taste (f) of the bacon. The data is shown in the table. Leanness 1 1.5 2.6 3.4
Eight children had their IQ measured and then took a general knowledge test. Their IQ, (x), and their marks, (y), for the test were summarised as follows: - 973 120 123. - 490 - 33.000 - 61595. a
In a training scheme for young people, the average time taken for each age group to reach a certain level of proficiency was measured. The data are shown in the table. Age x (years) 16 17 18 19 20 21
The following product moment correlation coefficients were calculated i-0.96 ii-0.35 Write down the coefficient that a shows the least correlation, iii 0 iv 0.72 b shows the most
Here are some product moment correlation coefficients. i-1, ii-0.5, iv 0.5, v AppendixLO1
Write down which one shows a perfect negative correlation, b zero correlation.AppendixLO1
Ahmed works out the product moment correlation coefficient between the heights of a group of fathers and the heights of their sons to be 0.954. Write down what this tells you about the relationship
Maria draws some scatter diagrams. They are shown below. Write down which scatter diagram shows: i a correlation of +1, ii a correlation that could be described as strong positive correlation, iii a
Jake finds that the product moment correlation coefficients between two variables x and y is 0.95. The product moment correlation coefficient between two other variables s and I was -0.95. Discuss
Patsy collects some data to find out if there is any relationship between the numbers of car accidents and computer ownership. She calculates the product moment correlation coefficient between the
Raj collects some data to find out whether there is any relationship between the height of students in his year group and the pass rate in driving tests. He finds that there is a strong positive
Coding is to be used to work out the value of the product moment correlation coefficient for the following sets of data. Suggest a suitable coding for each. a x 2000 2010. 2015 2005 2003 2006 y 3 6
For the two variables x and y the coding of A =x-7 and B-y-100 is to be used. The product moment correlation coefficient for A and B is found to be 0.973. What is the product moment correlation
Use the coding: p = x and q = y- 100 to work out the product moment correlation coefficient for the following data. x 0 5 3 2 1 100 117 112 110 106 AppendixLO1
The product moment correlation is to be worked out for the following data set using coding. x 50 40 55 45 60 4 y 3 5 4 6 a Using the coding p = and t = y find the values of Spp, S., and Spr- b
The tail length (t cm) and the mass (m grams) for each of eight woodmice were measured. The data is shown in the table. t (cm) 8.5 7.5 8.6 7.3 8.1 7.5 8.0 7.8 m (g) 28 22 26 21 25 20 20 22 a Using
A shopkeeper thinks that the more newspapers he sells in a week the more sweets he sells. He records the amount of money (m pounds) that he takes in newspaper sales and also the amount of money he
The following table shows the distance (x) in miles and the cost (y) in pounds of each of 10 taxi journeys. x (miles) 8 6.5 4 2.5 y (pounds) 10.2 8.8 5.5 9 2 10 4.5 7.5 7.2 5.7 7.4 11.0 5.2 12.0 6.4
The following scatter diagrams were drawn.a State whether each shows positive, negative or no correlation. b Interpret each scatter diagram in context.AppendixLO1 Length i Length and age ii
The following scatter diagrams were drawn by a student.The student calculated the product moment correlation coefficient for each set of data. The values were: a -0.12 b 0.87 c -0.81 Write down which
The product moment correlation coefficient for a person's age and his score on a memory test is -0.86. Interpret this value.AppendixLO1
Wai wants to know whether the 10 people in her group are as good at Science as they are at Art. She collected the end of term test marks for Science (s), and Art (a), and coded them using x and y =
Nimer thinks that oranges that are very juicy cost more than those that are not very juicy. He buys 20 oranges from different places, and measures the amount of juice (j ml), that each orange
The following table shows the values of two variables v and m. v 50 70 60 82 45 35 110 70 35 30 m 140 200 180 210 120 100 200 180 120 60 The results were coded using x-v-30 and y- m 20 a Complete the
Each of 10 cows was given an additive (x) every day for four weeks to see if it would improve their milk yield (y). At the beginning the average milk yield per day was 4 gallons. The milk yield of
The following table shows the engine size (c), in cubic centimetres, and the fuel consumption (f), in miles per gallon to the nearest mile, for 10 car models. c (cm) 1000 1200 1400 1500 1600 1800
In a study on health, a clinic measured the age, (a years), and the diastolic blood pressure, (din mm of mercury), of eight patients. The table shows the results. a (years) 20 35 50 25 60 45 25 70 d
An NHS trust has the following data on operations. Number of operating theatres 5 6 7 8 Number of operations carried out per day 25 30 35 40 Which is the independent and which is the dependent
A park ranger collects data on the number of species of bats in a particular area. Number of suitable habitats 10 24 28 Number of species 1 2 3 Which is the independent and which is the dependent
The equation of a regression line in the form y = a + bx is to be found. Given that S = 15, Sy 90, 3 and 15 work out the values of a andb. =AppendixLO1
Given S = 30, S., 165, 4 and y = 8 find the equation of the regression line of y on x.AppendixLO1
The equation of a regression line is to be found. The following summary data is given. S = 40, Sy = 80, x=6, y=12. Find the equation of the regression line in the form y = a + bx.AppendixLO1
Data is collected and summarised as follows. = 10 Ex-30 Sy=48 Day 140 4. a Work out,, S, and Sy b Find the equation of the regression line of y on x in the form ya+ bx.AppendixLO1
For the data in the table: 2 4 8 10 y 3 7 8 13 17 a calculate S, and S b find the equation of the regression line of y on x in the form y = a + bxc.AppendixLO1
A field was divided into 12 plots of equal area. Each plot was fertilised with a different amount of fertilizer (h). The yield of grain (g) was measured for each plot. Find the equation of the
An accountant monitors the number of items produced per month by a company (n) together with the total production costs (p). The table shows these data. Number of items, 1, (1000s) 21 39 48 24 72 75
The relationship between the number of coats of paint applied to a boat and the resulting weather resistance was tested in a laboratory. The data collected are shown in the table. 1 2 3 4 5 Coats of
Given that the coding p = x + 2 and q =y-3 has been used to get the regression equation p+q= 5 find the equation of the regression line of y on x in the form y = a + bxc.AppendixLO1
Given the coding x = p- 10 and y = s - 100 and the regression equation x = y + 2 work out the equation of the regression line of s on p.AppendixLO1
Given that the coding gand h=-2 has been used to get the regression equation h=6-4g find the equation of the regression line of y on x.AppendixLO1
The regression line of t on s is found by using the coding xs-5 and y =t-10. The regression equation of y on x is y = 14+3x. Work out the regression line of t on s. =AppendixLO1
A regression line of c on d is worked out using the coding x and y = d a Given Sy - 120, S. 240, the mean of x (x) is 5 and the mean of y ) is 6, calculate the regression line of y on x. b Find the
Some data on heights (h) and weights (w) were collected. The results were coded such that x = h-8. 2 and y = . The coded results are shown in the table. x 1 5 10 16 17 y 9 12 16 21 23 a Calculate S.,
Given the regression line y = 24-3x find the value of y when x is 6.AppendixLO1
The regression line for the weight (w) in grams on the volume (v) in cm for a sample of small marbles is w-300+ 12x Calculate the weight when the volume is 7 cm AppendixLO1
a State what is meant by extrapolation. b State what is meant by interpolation.AppendixLO1
12 children between the ages (x) of five and 11 years were asked how much pocket money (y) they were given each week. The equation for the regression line of y on x was found to be y=2x-8. a Use the
The pulse rates (y) of 10 people were measured after doing different amounts of exercise (x) for between two and 10 minutes. The regression equation y = 0.75x+72 refers to these data. The equation
Over a period of time the sales, (y) in thousands, of 10 similar text books and the amount, (x) in thousands, spent on advertising each book were recorded. The greatest amount spent on advertising
Research was done to see if there is a relationship between finger dexterity and the ability to do work on a production line. The data is shown in the table. Dexterity Score (x) 2.5 Productivity (y)
A metal rod was found to increase in length as it was heated. The temperature (t) and the increase in length (mm) were measured at intervals between 30C and 400C degrees. The regression line of I on
Two variables s and t are thought to be connected by a law of the form t=a+bs, where a and b are constants. a Use the summary data: = 553 7=45.75 549 S = 6193 Est 31185 n 12 5 46.0833 to work out the
A biologist recorded the breadth (x cm) and the length (y cm) of 12 beech leaves. The data collected can be summarised as follows. 2x = 97.73 Ex = 33.1 a Calculate S, and Sy Sy=66.8 = 195.94 b Find
Energy consumption is claimed to be a good predictor of Gross National Product. An economist recorded the energy consumption (x) and the Gross National Product (y) for eight countries. The data are
In an environmental survey on the survival of mammals the tail length t (cm) and body length m (cm) of a random sample of six small mammals of the same species were measured. These data are coded
A health clinic counted the number of breaths per minute (r) and the number of pulse beats (p) per minute for 10 people doing various activities. The data are shown in the table. The data are coded
A farm food supplier monitors the number of hens kept (x) against the weekly consumption of hen food (y kg) for a sample of 10 small holders. He records the data and works out the regression line for
Water voles are becoming very rare; they are often confused with water rats. A naturalist society decided to record details of the water voles in their area. The members measured the weight (y) to
A mail order company pays for postage of its goods partly by destination and partly by total weight sent out on a particular day. The number of items sent out and the total weights were recorded over
Write down whether or not each of the following is a discrete random variable. Give a reason for your answer. a The average lifetime of a battery. b The number of days in a week. c The number of
A fair die is thrown four times and the number of times it falls with a 6 on the top, Y, is noted. Write down all the possible values of y.AppendixLO1
A bag contains two discs with the number 2 on them and two discs with the number 3 on them. A disc is drawn at random from the bag and the number noted. The disc is returned to the bag. A second disc
A discrete random variable X has the following probability distribution: 1 2 3 4 + k P(X-x) Find the value of k.AppendixLO1
The random variable X has a probability function P(X = x)=kx Show that k x=1, 2, 3, 4.AppendixLO1
The random variable X has the probability function P(X = x) = *--1 x = 1, 2, 3, 4,AppendixLO1
Construct a table giving the probability distribution of X.AppendixLO1
The random variable X has a probability function kx P(X-2) Alx-1) where k is a constant. a Find the value of k. * 1,3 *-2,4 b Construct a table giving the probability distribution of X.AppendixLO1
The discrete random variable X has a probability function. 0.1 x -2,-1 *-0,1 0.2 *-2 P(X-x)-8 a Find the value of . b Construct a table giving the probability distribution of X.AppendixLO1
A discrete random variable has the probability distribution shown in the table below. 01 I P(X x)-a 2 a +4 Find the value of a.AppendixLO1
A discrete random variable X has probability distribution * 0 1 2 3 4 5 P(X = x) 0.1 0.1 0.3 0.3 0.1 0.1 a Find the probability that X 3. c Find the probability that 1 < x < 4.AppendixLO1
A discrete random variable X has probability distribution x 0 1 2 3 1 1 P(X = x) x 2 Find a P(1 < x < 3), b P(X < 2). 3 A discrete random variable X has a probability distribution 1 2 3 4 5 6 * P(X =
A discrete random variable has a cumulative distribution function F(x) given in the table. * F(x) 012345 6 0 0.1 0.2 0.45 0.5 0.9 1 a Draw up a table to show the probability distribution X. b Write
The random variable X has a probability function P(X-1){ 1xx x 1, 3, 5 k(x-1) x 2, 4, 6 where k is a constant. a Find the value of k. b Draw a table giving the probability distribution of X. Find P(2X
The discrete random variable X has the probability function x=-2,-1 0.1 P(X-x) 0.3 * 0,1 x-2 a Find the value of a b Draw a table giving the probability distribution of X. c Write down the value of
The discrete random variable X has a cumulative distribution function F(x) defined by 0 x=0 F(x) 1+x x-1, 2, 3, 4, 5 6 1 x>5 a Find P(X4). b Show that P(X-4) is c Find the probability distribution
The discrete random variable X has a cumulative distribution function F(x) defined by 0 x=0 (x + k) Fix)- x-1, 2 and 3 16 1 x>5 a Find the value of k. b Find the probability distribution for
Find E(X) and E(X2) for the following distributions of x. a $ 2 4 6 8 P(X = x) 0.3 0.3 0.2 0.2 b 1 2 3 4 P(X = x) 0.1. 0.4 0.1 0.4 AppendixLO1

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