Statistics and Probability Answers

It is claimed that watching television reduces the amount of physical exercise, causing weight gains. A sample of 15 children was taken. The number of kilograms each child was overweight (a negative number indicates the child is underweight) and the number of hours the television viewing per week were recorded. The data are listed in the table.

Television Viewing (hours)

42

34

25

35

37

38

31

33

19

29

Overweight (kg)

18

6

-1

13

14

7

7

-9

8

Additional Information: SST = Σ(𝑌−𝑌̅)2 = 572.10, SSE = Σ(𝑌−𝑌̂)2 = 149.75

a) Compute the coefficients of the sample regression line.

b) Interpret the estimated slope coefficient.

c) Determine and interpret the coefficient of determination and test whether the model is good or not?

d) Test whether there is evidence of a negative linear relationship between the number of hours of television viewing per week and the child's overweight using 1 per cent level of significance.

Bank customers arrive randomly on week days afternoon at an average of 3.2 customers every 4 minutes. What is the probability of having more than 7 customers in a 4 minute interval on a week day afternoon?

An author has prepared to submit six books for publication. The probability of any book being accepted is 0.20, assuming independence, find the probability that the author will have:

(i) Exactly one book accepted.

(ii) At least two books accepted.

(iii) At most two books accepted.

A client company of your firm is a horticultural shop selling a wide variety of products to its customers. The analysis of weekly sales of plants throughout the year is summarized in the following frequency distribution:

Weekly sales of plants ($'000) Number of weeks

12.55 but less than 12.80 9

12.80 but less than 13.05 19

13.05 but less than 13.30 10

13.30 but less than 13.55 8

13.55 but less than 13.80 6

Required:

(a) Construct a cumulative frequency distribution curve (5 marks)

(b) Calculate the mean,modal and median weekly sales of plants for the horticultural shop. (8 marks)

(c) Determine the variance and standard deviation of the weekly sales of plants for the horticultural shop. (6 marks)

(d) Calculate the coefficient of variation and coefficient of skewness for the weekly sales of plants for the horticultural shop. ( 6 marks)

(Total: 25 marks)

A survey commissioned to assess whether people in some country would welcome the constitution of a commission of inquiry into the Privatization process of that country which took place two decades ago reported that 51% of the respondents felt it was total wastage of the already constrained country's resources. Of the respondents who were age 45 or older, 70% believed the commission of inquiry was necessary. Of the people surveyed,57% were under age of 45. One respondent is selected randomly.

(i) What is the probability that the person is younger than age 45 and believes that the commission of inquiry is necessary?

(ii) If the person selected believes that the commission of inquiry is necessary, what is the probability that the person is 45 years old or older?

(iii)What is the probability that the person is younger than age 45 or believes the commission of inquiry is necessary?

A contractor estimates the probabilities for the number of days required to complete a certain type of project as follows:

Time (days) 1 2 3 4 5

Probability 0.04 0.21 0.34 0.31 0.10

(1) what is the probability that a randomly chosen project will take less than 3 days to complete?

(2) Find the expected time to complete a project.

(3) Find the standard deviation of time required to complete a project.

(If the contractor's project cost is made up of two parts: a fixed cost of $100 million plus $10 million for each day taken to complete the project, find the variance of total project costs.

Robert has attended 32 out of 40 after-school band practices this year. Based on his record of attendance, which is the probability that Robert will attend band practice in the future?

Graded AssignmentUnit Test, Part 2: Linear Models

Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit.

Please make certain to show your work as part of your grade is associated with showing the steps to complete a problem. You want to set things up so that someone else can see the process you used to arrive at your answer.

Total score: ____ of 15 points

(Score for Question 1: ___ of 6 points)

1.    A poll asked 15 pet owners what kind of pet they have and whether they feed their pet kibble or meat. The results are recorded in the table.

<b><span style="font-size:12.0pt;color:black;mso-themecolor:text1">Person<o:p></o:p></span></b>

Pet

Food

1

Cat

Kibble

2

Cat

Kibble

3

Dog

Kibble

4

Cat

Meat

5

Dog

Meat

6

Dog

Kibble

7

Dog

Meat

8

Dog

Meat

9

Catr

Meat

10

Cat

Meat

11

Dog

Meat

12

Cat

Kibble

13

Dog

Meat

14

Cat

Kibble

15

Dog

Meat

(a)  Create a two-way table of the data. Of the pet owners surveyed, how many owned dogs? How many fed their pets meat?

a.    Please include labels and totals.

(b)  Create a two-way relative frequency table that displays the relative frequency of the cat owners and dog owners who fed their pets kibble or meat. Express your answers as decimals written to three decimal places.

(c)  What is the percentage of dog owners who fed their pets meat?

Answer:

Part A, How many owned dogs?

Part A, How many fed their pets meat?

Part C

Two way table, Part A

Kibble

Meat

Total

Cat

Dog

Total

Relative frequency table, Part B

Kibble

Meat

Total

Cat

Dog

Total

Note: these tables are asking for two different things. Please review 1.02, and come into Math Help Lab, if you’re unsure what the difference is or otherwise need assistance.

(Score for Question 2: ___ of 5 points)

2.    Consider this scatter plot.

Test Scores in Relation to Homework

Test Scores

Hours of Homework

(a)  Is the relationship linear or not linear? Justify your response.

(b)  Is the relationship increasing or decreasing? Find the slope and use it to help justify your answer.

(c)  Paul uses the function y = 7x + 30 to model the situation. What score does Paul’s model predict for 3 hours of homework? Hint: It’s _not_ asking you to use the graph.

(d)  Describe what the number 30 in Part (c) mean in the context of the situation? Hint: Think about what kind of function equation you have in Part C.

Answer:

Part A)

Part B)

Part C)

Part D

The probability density function of a random variable X is given by :

f(x)={kx(2-x), 0<x<2

{0, e.w

a) Find the value of k

b)Find the distribution function F(X)

c)Find P(X>3)

roll a fair die twice. let x be the random variable that gives the absolute value of the different between the two number. a)construct the probability distribution of the variable x. b) find the cumulative distribution function.