Statistical Related Questions

everblazing

question_6.pdf

Home >Applied Sciences homework help >Statistical Related Questions

Sample Questions

Chart reading, Probability and Binomial Distribution

(Lectures 2 & 6)

Question 1. (14 marks) PLEASE SHOW ALL OF YOUR WORKING OUT

On a particularly dangerous intersection, the number of accidents on every day for an entire year is recorded

The data showing how many days experience different numbers of accidents is presented on the left

(2 marks) 1a. What is the probability of having a day with no accident ?

(3 marks) 1b. Determine the expected number of accidents per day.

(5 marks) 1c. Determine the population standard deviation of the number of accidents per day ?

(2 marks) 1d. Does the number of accidents per day follow a normal distribution ? Give reasons for your answer ?

(2 marks) 1e. What distribution could be used to study number of days with no accident over a 2 week period ? Give reasons for your choice ?

Question 2. (14 marks) PLEASE SHOW ALL OF YOUR WORKING OUT

A particular city store is reviewing the number of shoplifters caught in the store on every day of a shopping year. The histogram at the left shows the number of shop lifters caught in the store, and how many days for each number of shop lifters caught.

(2 marks) 2a. What is the probability of having a day with no shop lifter ?

(3 marks) 2b. Determine the expected number of shop lifters caught per day.

No of shop lifters caught in store per day

Number of Shop Lifters

N u

m b

e r

o f D

a ys

0 1 2 3 4 5

0 5

0 1

0 0

1 5

0 2

0 0

100

146

3 0

(5 marks) 2c. Determine the population standard deviation of the number of shop lifters caught per day ?

(2 marks) 2d. Does the number of shop lifters caught per day follow a normal distribution ? Give reasons for your answer ?

(2 marks) 2e. What distribution could be used to study number of days with more than 1 shop lifter caught over a 2 week period ? Give reasons for your choice ?

Question 3. (10 marks) PLEASE SHOW ALL OF YOUR WORKING OUT

On a particularly busy intersection, the number of people who run a red light in a dangerous manner on every day for an entire year is recorded

The data showing how many days experience different numbers of dangerously run red lights is presented on the left

(2 marks) 3a. What is the probability of having a day with no red light run ?

(2 marks) 3b. Determine the expected number of red lights run per day.

(3 marks) 3c. Determine the population standard deviation of the number of red lights run per day ?

(2 marks) 3d. Does the number of red lights run per day follow a normal distribution ? Give reasons for your answer ?

(2 marks) 3e. What distribution could be used to study number of days with no accident over a 2 week period ? Give reasons for your choice ?

Question 4. (14 marks) PLEASE SHOW ALL OF YOUR WORKING OUT

The number of customers in a typical city restaurant was recorded every open day for a whole year (in total the restaurant was open 312 days). A summary is provided in the chart below.

No of people who dangerously run a red light

Number of Dangerously Run Red Lights

N u

m b

e r

o f D

a ys

0 1 2 3 4 5

0 5

0 1

0 0

1 5 0

2 0 0

133 137

0 0

(2 marks) 4a. How many days experienced between 110 and 130 customers ? What proportion of the days is this ?

(3 marks) 4b. Determine the expected number of customers per day ?

(2 marks) 4c. What is the mode of the histogram ? What does this mean ?

(2 marks) 4d. Estimate the probability of having more than 90 customers in a day ?

(3 marks) 4e. Assuming that the probability of having more than 90 customers is fixed, What is the probability of having at least one day in three with more than 90 customers ?

(2 marks) 4f. What distribution would we expect to describe the probabilities that over the next 10 days, there will be (0...10) days of more than 90 customers a day ? Why ?

Question 5. (14 marks) PLEASE SHOW ALL OF YOUR WORKING OUT

The number of customers in a typical city restaurant was recorded every open day for a whole year (in total the restaurant was open 312 days). A summary is provided in the chart below.

Daily Customer Numbers

Customers

N u

m b

e r

o f

D a

40 60 80 100 120 140

0 5

0 1

0 0

1 5

0 2

0 0

1 9

198

25 3

(2 marks) 5a. How many days experienced between 70 and 110 customers ? What proportion of the days is this ?

(3 marks) 5b. Determine the expected number of customers per day ?

(2 marks) 5c. What is the mode of the histogram ? What does this mean ?

(2 marks) 5d. Estimate the probability of having less than 70 customers in a day ?

(3 marks) 5e. Assuming that the probability of having less than 70 customers is fixed, What is the probability of having at least one day in three with less than 70 customers ?

(2 marks) 5f. What distribution would we expect to describe the probabilities that over the next 10 days, there will be (0...10) days of less than 70 customers a day ? Why ?

Question 6. (14 marks) PLEASE SHOW ALL OF YOUR WORKING OUT

The number of customers in a typical city restaurant was recorded every open day for a whole year (in total the restaurant was open 312 days). A summary is provided in the chart below.

Frequency of Daily Customer Number

Customers per day

N u

m b

e r

o f

d a

y s

40 60 80 100 120 140

0 2

0 4

0 6

0 8

0 1

0 0

89 82

(2 marks) 6a. How many days experienced between 90 and 130 customers ? What proportion of the days is this ?

(3 marks) 6b. Determine the expected number of customers per day ?

(2 marks) 6c. What is the mode of the histogram ? What does this mean ?

(2 marks) 6d. Estimate the probability of having less than 70 customers in a day ?

(3 marks) 6e. Assuming that the probability of having less than 70 customers is fixed, What is the probability of having at least one day in three with less than 70 customers ?

(2 marks) 6f. What distribution would we expect to describe the probabilities that over the next 10 days, there will be (0...10) days of less than 70 customers a day ? Why ?

Question 7. (14 marks) PLEASE SHOW ALL OF YOUR WORKING OUT

The number of customers at a typical small general store was recorded every open day for a whole year (in total the store was open 312 days). A summary is provided in the chart below.

(2 marks) 7a. How many days experienced between 750 and 810 customers ? What proportion of the days is this ?

(3 marks) 7b. Determine the expected number of customers per day ?

(2 marks) 7c. What is the mode of the histogram ? What does this mean ?

(2 marks) 7d. Estimate the probability of having less than 690 customers in a day ?

(3 marks) 7e. Assuming that the probability of having less than 690 customers is fixed, What is the probability of having at least one day in three with less than 690 customers ?

(2 marks) 7f. What distribution would we expect to describe the probabilities that over the next 10 days, there will be (0...10) days of less than 690 customers a day ? Why ?

Question 8. (14 marks) PLEASE SHOW ALL OF YOUR WORKING OUT

A new restaurant was opened, and the number of customers per day measured for the first 366 days that it is open. The measurements were plotted on a time series as shown,

8a. Describe any trends in the time series ? (2 marks)

8b. Make two inferences about the expected number of customers in the next 366 days after those considered ?

(2 marks)

A histogram of the number of customers per day was determined based on this data, as shown below

8c. How many days experienced between 50 and 150 customers? What proportion of the days is this? (2 marks)

8d. Determine the expected number of customers per day? (3 marks)

8e. Estimate the probability of having less than 100 customers in a day? (2 marks)

8f. We wish to study the number of days of less than 100 customers over a two week period. What distribution would we expect to describe the probabilities of having a number of days with less than 100 customers in a 14 day period ? Why, give at least 2 reasons ?

(3 marks)

Question 9. (14 marks) PLEASE SHOW ALL OF YOUR WORKING OUT

A new restaurant was opened, and the number of customers per day measured for the first 366 days that it is open. The measurements were plotted on a time series as shown,

9a. Describe any trends in the time series ? (2 marks)

9b. Make two inferences about the expected number of customers in the next 366 days after those considered ?

(2 marks)

A histogram of the number of customers per day was determined based on this data, as shown below

9c. How many days experienced between 100 and 150 customers? What proportion of the days is this? (2 marks)

9d. Determine the expected number of customers per day? (3 marks)

9e. Estimate the probability of having less than 100 customers in a day? (2 marks)

9f. We wish to study the number of days of less than 100 customers over a two week period. What distribution would we expect to describe the probabilities of having a number of days with less than 100 customers in a 14 day period ? Why, give at least 2 reasons ?

(3 marks)

QUESTION 10 (14 MARKS)

Please Show All Of Your Working Out

A new costume jewelery store was opened, and the number of customers purchasing goods per day was counted for the first 366 days that it is open. The measurements were plotted on a time series as shown,

Time series for the Number of customers between days 100 and 150 are shown below so that the higher frequency behavior can be seen:

10a. Describe any trends in the time series between days 100 and 150 ? (2 marks)

10b. Make two inferences about the expected number of customers in the next 366 days after those considered ?

(2 marks)

A histogram of the number of customers per day was determined based on this data, as shown below

10c. How many days experienced between 50 and 150 customers? What proportion of the days is this? (2 marks)

10d. Determine the expected number of customers per day? (3 marks)

10e. Estimate the probability of having less than 250 customers in a day? (2 marks)

10f. Using the Binominal distribution, we model the number of days with less than 250 customers out of any 7 day period. What is the probability of having less than 250 customers per day on 5 days out of 7 ?

(3 marks)

Question 11. (14 marks) PLEASE SHOW ALL OF YOUR WORKING OUT

Time series for the Number of customers between days 100 and 150 are shown below so that the higher frequency behavior can be seen:

11a. Describe any trends in the time series for the first 366 days ? (2 marks)

11b. Make two inferences about the expected number of customers in the next 366 days after those considered ?

(2 marks)

A histogram of the number of customers per day was determined based on this data, as shown below

11c. How many days experienced between 25 and 175 customers? What proportion of the days is this? (2 marks)

11d. Determine the expected number of customers per day? (3 marks)

11e. Estimate the probability of having more than 175 customers in a day? (2 marks)

11f. Using the Binominal distribution, we model the number of days with more than 175 customers out of any 7 day period. What is the probability of having more than 175 customers per day on 5 days out of 7 ?

(3 marks)

QUESTION 12 (14 MARKS)

Please Show All Of Your Working Out

A new atrium store selling figurines opened in the atrium of a suburban shopping center, and the number of customers purchasing goods per day was counted for the first 366 days that it is open. The measurements were plotted on a time series as shown,

Time series for the Number of customers between days 100 and 150 are shown below so that the higher frequency behavior can be seen:

12a. Describe any trends in the time series between days 100 and 150 ? (2 marks)

12b. Make two inferences about the expected number of customers in the next 366 days after those considered ?

(2 marks)

A histogram of the number of customers per day was determined based on this data, as shown below

12c. How many days experienced between 65 and 75 customers? What proportion of the days is this? (2 marks)

12d. Determine the expected number of customers per day? (3 marks)

12e. Estimate the probability of having less than 65 customers in a day? (2 marks)

12f. Using the Binominal distribution, we model the number of days with less than 65 customers out of any 7 day period. What is the probability of having less than 65 customers per day on 5 days out of 7 ?

(3 marks)