# Business Statistics || Fall 2016 || Pokhara University

 Level:  Bachelor Semester – Fall Year: 2016 Programme: BBA/BBA-BI/BBA-TT/BCIS Full Marks: 100 Course: Business Statistics Pass Marks: 45 Time:  3hrs.

 Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

Section “A”

Attempt all the questions.

10×2

1. Calculate the range and the coefficient of range of the following data set.

2,3,5,7,12,8,10,13,20,16,15

2. In a moderately asymmetrical distribution, the mean and median are 20 and 23. Find mode.
3. For a binomial distribution with n=4 and p=0.45. Find p(x=2).
4. Let X N(0,1),then find P(-0.5 .
5. What are the two differences between primary and secondary data?
6. If Zstat =2, what is P-value?
7. Construct a stem-and-leaf diagram of the monthly income (Rs. ’00) of 10 people. 325, 210, 350, 400, 478, 560, 600, 515, 370, 250
8. Define mutually exclusive and independent events.
9. A box of one dozen eggs contains one bad egg. If three eggs are chosen at random, what is the probability that one of them will be bad?
10. Define null and alternative hypotheses with an example.
Section “B”

Attempt any six questions

6×10

11. a)       100 students took a test. The result of those who secured less than 60% mark is given below:

Marks                      0-20          20-40         40-60

No. of students        16              24              30

If  the average mark of all students was 50, find out  the average marks of those  who secured more than 60% marks

b)      In order to estimate how much water will be needed to supply for the Baneshwor area in Kathmandu valley in the next year, the town council asked to find out how much water a sample of families currently uses. The sample of 15 families used the following number of gallons (in thousands) in the past year:

 11.2 21.5 16.4 19.7 14.6 16.9 32.2 18.2 13.1 23.8 18.3 15.5 18.8 22.7 14

i)                    List the five-number summary.

ii)                  Form the Box and Whisker plot, determine the shape of the distribution.

12. a)       The following table presents a summary of the responses to two questions: “Was a particle found on the die that produced the wafer?” and “Is the wafer good or bad?”

 Quality of wafer Condition of die No particles Particles Totals Good 320 14 334 Bad 80 36 116 Totals 400 50 450

If a wafer is selected at random, what is the probability that

it was produced from a die with no particle?

(i)     It was a bad wafer and was produced from a die with no particles?

(ii)   Suppose a wafer is bad, what is the probability that it was produced from a die with particles?

b)      An insurance company insured 2000 scooter drivers, 4000 car drivers, and 6000 truck drivers. The probabilities of their accident by scooter, car, and truck are 0.1, 0.3, and 0.2 respectively. One of the insured persons meets with an accident

(i)     What is the probability that he is a scooter driver?

(ii)    What is the probability that he is a truck driver?

13. a)       The monetary benefit paid to the employees of a firm are given below:

 Monetary benefit 75 100 150 200 400 No. of employees 30 25 20 15 10

Construct the probability distribution of the above data. Find the expected monetary benefit and its standard deviation.

b)      A multiple–choice test has 5 questions there are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly. What is the probability that he will get?

i.         Five questions correct?

ii.         At least four questions correct?

14. a)       The average number of network errors experienced in a day on a local area network (LAN) is distributed with an average of 4. What is the probability that in any given day?

(i)                 Zero network errors will occur?

(ii)               Exactly one network errors will occur?

(iii)             At least one network errors will occur?

b)      The income of a group of  20,000 persons was found to be normally distributed with a mean of Rs. 7,500 and a standard deviation of Rs.500.Find

(i)                 The lowest income of the richest 20% of persons.

(ii)               The highest income of the poorest 10% of persons.

15. a)       A mineral water company has launched a new 10-liter bottle in the urban market. After some time, the firm receives some complaints that the bottles do not contain exactly 10 liters. For verifying this complaint, the company’s investigating team has taken a random sample of 120 bottles from different places. The sample mean is computed as 9.5 and the sample standard deviation is computed as 1.1. Construct a 95% confidence interval to estimate the mean for the population.

b)      An insurance company, based on past experience, estimates the mean damage for a natural disaster in its area is \$5,000. After introducing several plans to prevent the loss, it randomly samples 200 policyholders and finds the mean amount was \$4,800 with a standard deviation of \$1,300. Does it appear the prevention plans were effective in reducing the mean amount of claim? Use 0.05 significance level.

16. a)       A sample of 500 respondents was selected in a large metropolitan area to determine the various information concerning consumer behavior. Among the questioned, asked was “Do you enjoy shopping for clothing?” Of 240 males 136 answered yes. Of 260 females, 174 answered yes. Is there evidence of a significant difference between males and females in the proportion that enjoy shopping for clothing at 0.01 level of significance?

b)      Find Ginni’s coefficient of mean difference for the following data300,700,100,750,400 and 800.

17. a)       From the following Steam and Leaf display regarding the age of Glaucoma patients treated in Tilganga Eye Institute, Kathmandu, construct a histogram using a class width of 10. Also, prepare less than ogive and find the percentage of patients below 68 years ago.

Steam           leaves

4           0    2     3    4    6

5           0     1     2    5    5   7

6           0     1     2    3    5   5   5    7    8   9   9

7           1     2     4    5    8

8           0      4     7

9               1     5     8

b)      Describe the difference between descriptive and inferential statics.

18.

Section “C”

Case Analysis

a)       Banks are permitted to sell a form of life insurance called savings bank life insurance (SBLI). the approval process consists of underwriting, which includes a review of the application, a medical information bureau check, a possible request for additional medical and medical exams, and a policy compilation stage during which the policy pages are generated and sent to the bank for delivery.  the ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. during a period of one month, a random sample of 27 approved policies was selected, and the following total processing times in days were recorded; the data are 73  19  16  64  28  28  31  90   60  56  31  56  22  18  45  48  17  17   17  91  92  63  50  51  69  16  17 where

i)        Construct 95% confidence interred of the population mean waiting time.

ii)      Is it reasonable to conclude that the average waiting time is more than 45 days.

b)      A stock market is very crucial to sustainable economic growth as it can assure the flow of resources to the most productive investment opportunities. The market price of a share is a key factor that influences the investment decisions of stock market investors. The share price is one of the most important indicators available to the investors for their decision to invest in or not a particular share. Most of the investors of the Nepalese share market have no significant knowledge about the pricing behavior of the stock market as a result they invest on the basis of rumors.

Mr. Prakshit Joshi is planning to invest in the share market and visits a financial advisor to get advice. Mr. Joshi, dear consultant! “I have ten lakh rupees on saving account on NABIL bank limited but I am getting 3.5% per year interest rate. I am thinking to invest it in the share market so that it will provide a better return than shaving account.”

Consultant, Well Mr. Joshi! Great idea. Following are some listed companies whose share price of March 2016 has been listed below. Wait for a while, I will check the consistency of their price and advice you to invest in a more consistent market.

 Day SBL SCBNL EBL 17 599 2580 2050 1 605 2439 2035 18 602 2575 2055 2 620 2480 2080 19 604 2590 2155 3 619 2525 2085 20 614 2555 2134 4 627 2515 2065 21 602 2524 2145 5 606 2514 2055 22 622 2532 2125 6 615 2485 2015 23 624 2565 2124 7 618 2425 2035 24 634 2620 2199 8 625 2481 2025 25 632 2690 2300 9 623 2535 2042 26 642 2698 2314 10 615 2556 2034 27 648 2695 2318 11 629 2514 2080 28 642 2728 2400 12 625 2485 2085 29 648 2715 2460 13 626 2425 2065 30 642 2675 2375 14 594 2515 2034 15 588 2565 2055 16 605 2570 2035

Summary calculation

 SBL SCBNL EBL Sum of share price 18595 76771 63979 Sum of the square of share price 11533187 196671673 136907429 Median share price 621 2545 2080

Questions

a)       If you are the financial consultant which company has a consistent share price in March 2016?

b)      Which company do you suggest for investment to Mr. Joshi and Why?

c)       Comment on the shape of the distribution of share price of March 2016.

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