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Statistics and Probability

The management of ‘Fun Land’ studied the waiting times for Dogging Car by children in waiting area before sit and drive a car. The following data with waiting times in minutes were collected over a one-month period. Consider the following data in Table 2.1:

Table 2.1

28 17 30 25 22

33 38 23 26 10

14 15 24 22 34

12 33 32 31 26

26 32 35 17 12

34 32 22 19 14

15 27 15 25 31

36 28 35 28 22

26 10 29 19 15

9 20 34 27 20

a) Develop a frequency distribution using classes of 9–14, 15–20, 21–26, 27–32, and 33–38. [1]

b) Develop a relative frequency distribution and a percent frequency distribution. [2]

c) Cumulative frequency and a cumulative relative frequency. [2]

Table 2.1

28 17 30 25 22

33 38 23 26 10

14 15 24 22 34

12 33 32 31 26

26 32 35 17 12

34 32 22 19 14

15 27 15 25 31

36 28 35 28 22

26 10 29 19 15

9 20 34 27 20

a) Develop a frequency distribution using classes of 9–14, 15–20, 21–26, 27–32, and 33–38. [1]

b) Develop a relative frequency distribution and a percent frequency distribution. [2]

c) Cumulative frequency and a cumulative relative frequency. [2]

Statistics and Probability

According to the All Pakistan Software Developer Association (APSDA), developers generally spend more than 40 hours each week working on software and web development. The Table 4.1 shows the number of hours worked per week for a sample of 15 Software developers and a sample of 10 Web developers.

Table 4.1

Software Developers 56 54 54 49 61 48 58 60 59 53 50 58 55 57 52

Web

Developers 47 50 46 47 48 49 46 55 44 42 ----

a) What is the third quartile of spending working hours for Software developers?

b) Create a box plot for the number of hours worked for Software developers.

c) Create a box plot for the number of hours worked for Web developers.

d) Comment on the differences between the box plots for Software & Web developers

Table 4.1

Software Developers 56 54 54 49 61 48 58 60 59 53 50 58 55 57 52

Web

Developers 47 50 46 47 48 49 46 55 44 42 ----

a) What is the third quartile of spending working hours for Software developers?

b) Create a box plot for the number of hours worked for Software developers.

c) Create a box plot for the number of hours worked for Web developers.

d) Comment on the differences between the box plots for Software & Web developers

Statistics and Probability

The management of ‘Fun Land’ studied the waiting times for Dogging Car by children in waiting area before sit and drive a car. The following data with waiting times in minutes were collected over a one-month period. Consider the following data in Table 2.1:

Table 2.1

28 17 30 25 22

33 38 23 26 10

14 15 24 22 34

12 33 32 31 26

26 32 35 17 12

34 32 22 19 14

15 27 15 25 31

36 28 35 28 22

26 10 29 19 15

9 20 34 27 20

a) Develop a frequency distribution using classes of 9–14, 15–20, 21–26, 27–32, and 33–38.

b) Develop a relative frequency distribution and a percent frequency distribution.

c) Cumulative frequency and a cumulative relative frequency.

Table 2.1

28 17 30 25 22

33 38 23 26 10

14 15 24 22 34

12 33 32 31 26

26 32 35 17 12

34 32 22 19 14

15 27 15 25 31

36 28 35 28 22

26 10 29 19 15

9 20 34 27 20

a) Develop a frequency distribution using classes of 9–14, 15–20, 21–26, 27–32, and 33–38.

b) Develop a relative frequency distribution and a percent frequency distribution.

c) Cumulative frequency and a cumulative relative frequency.

Statistics and Probability

On the basis of the previous record, an average of 4 accidents in one day occur on the superhighway during peak rush timings. Calculate the following if possible. If any part of question (you feel) is not possible to calculate give reason:

a. Evaluate the probability that on any Particular day there will be fewer than 3 accidents on this superhighway during the peak rush timings.

b. Compute the probability that on any Particular day there will be more than 6 accidents on this Super highway during the peak rush timings.

c. Find the Expected number of accidents per day and variance.

a. Evaluate the probability that on any Particular day there will be fewer than 3 accidents on this superhighway during the peak rush timings.

b. Compute the probability that on any Particular day there will be more than 6 accidents on this Super highway during the peak rush timings.

c. Find the Expected number of accidents per day and variance.

Statistics and Probability

Economists frequently make use of quintiles (i.e., the 20th, 40th, 60th, and 80th percentiles) particularly

when discussing incomes. Suppose that in a large city household incomes are normally distributed

with a mean of $50,000 and a standard deviation of $10,000. An economist wishes to identify the

quintiles. Unfortunately, he did not pass his statistics course. Help him by providing the quintiles.

Statistics and Probability

How much money does a typical family of four spend at a McDonald’s restaurant per visit? The amount is a normally distributed random variable with a mean of $16.40 and a standard deviation of $2.75.

a. Find the probability that a family of four spends less than $10.

b. What is the amount below which only 10% of families of four spend at McDonald’s?

Statistics and Probability

Sugar is packed in 5-pound bags. An inspector suspects the bags may not contain 5 pounds. A sample of 50 bags produces a mean of 4.6 pounds and a standard deviation of 0.7 pound. Is there enough evidence to conclude that the bags do not contain 5 pounds as stated, at α = 0.05? Also, find the 95% confidence interval of the true mean.

Statistics and Probability

a. Evaluate the probability that on any Particular day there will be fewer than 3 accidents on this superhighway during the peak rush timings.

b. Compute the probability that on any Particular day there will be more than 6 accidents on this Super highway during the peak rush timings.

c. Find the Expected number of accidents per day and variance.

Statistics and Probability

“Chief Grill” is a local restaurant, its annual data shows that the average sale of chicken steaks is 1200 serving per month with a standard deviation of 102. If the data is normally distributed; calculate the probability of sale of chicken steaks in the next month will be:

a. less than 1000 servings

b. more than 1400 servings

c. between 1100 to 1300 serving

d. less than 1000 but not less than 1350

a. less than 1000 servings

b. more than 1400 servings

c. between 1100 to 1300 serving

d. less than 1000 but not less than 1350

Statistics and Probability

The number of sample space when a regular dice is rolled twice, or when two dice are rolled together

what is it and write the sample space

what is it and write the sample space