# Business Statistics || Spring 2015 || Pokhara University

 Level:  Bachelor Semester – Spring Year: 2015 Program: 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.

## Attempt all the questions.

1. a)       BMT manufactures performance equipment for cars used in various types of racing. It has gathered the following information on the number of models of engines in different size categories used in the racing market it serves:

 Engine size in cubic inches Frequency(of models) 101-150 1 151-200 7 201-250 7 251-300 8 301-350 17 351-400 16 401-450 15 451-500 7

Construct a cumulative relative frequency distribution that will help answer these questions

1. Seventy percent of the engine models available are larger than about what size?
2. What was the approximate middle value in the original data set?

b)      Given the following stem-and-leaf display

 9 7  1  4 10 8  2  2  3  0 11 5  6  1  7  7  6  7 12 3  9  4  2  8  2 13 2  0

i.            Rearrange the leaves and form the revised stem and leaf display.

ii.            Place the data into an ordered array.

iii.            Which of these two devices seems to give more information? Give reasons.

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2. a)       From the following distribution of the marks of 500 students of a campus:

 Marks 0-20 20-40 40-50 50-60 60-80 80-100 No. of students 50 100 150 90 60 50

i.           Find the minimum pass mark if only 20% of the student had failed. Also, find the minimum marks obtained by the top 25% of the students.

ii.         Calculate the coefficient of variation and interpret its value.

b)         Summary Appliance Company has just completed a study of three possible assembly line configurations for producing its best-selling two-slice toasters. Configuration 1 has yielded a mean time to contrast a toaster of 34.8 minutes and a standard deviation of 4.8 minutes.  Configuration 2 has yielded a mean time of 25.5 minutes, and a standard deviation of 7.5 minutes. Configuration 3 has yielded a mean time of 37.5 minutes and a standard deviation of 3.8 minutes, which assembly line configuration has the least relative variation in the time it takes to construct a toaster?

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3. a)       The following table shows the survey results regarding the purchase behavior of force TVs and DVD players in the last six months of 300 households.

 Purchased Force Purchased DVD Yes No Total Force TV 38 42 80 Not Force TV 70 150 220 Total 108 192 300
1. Find the probability that if a household that purchased a television set is randomly selected the television set purchased is a Force TV.
2. Find the probability that a randomly selected household that purchases a Force TV and a DVD player.
3. What is the probability that they purchased a Force TV or DVD player?
4. What is the probability that a household purchased a DVD player give that household purchased a Force TV?

b)      A random variable x has the following probability distribution.

 X -2 -1 0 1 2 3 P(X) 0.2 k 0.1 2k k 0.3

Find value of k, E(X), E (4X + 5) and var(X)

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4. a)       The Machhapuchere Bank has recently started a new credit program. Customers meeting certain credit requirements can obtain a credit card accepted by participating area merchants that carry a discount. Past records show that 40% of all applicants for this card are rejected. If 8 applicants are selected, what is the probability that:

i.            Exactly 4 will be rejected?

ii.            At least two are rejected?

b)      The quality control manager of a certain company is inspecting a batch of chocolate chip cookies that have just been banked. If the production process is in control, the average number of chip parts per cookie is 6. What is the probability that in any particular cookies being inspected:

i.      None of the chip parts will be found?

ii.     At most two-chip parts will be found?

c)       The incomes of a group of 10000 persons were found to be normally distributed with a mean Rs. 75 and standard deviation of Rs. 5. Find the lowest income of the richest 10% of persons.

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5. a)       In a survey of 763 women who had started their own businesses, 229 said that they launched their business for greater freedom. Only 99 indicated that a desire to make more money drove them to start their business. Set up 90% confidence interval estimate of the population of women who start a new business to gain freedom.

b)      A random sample of 10 bulbs has the following life in months: 24, 26, 32, 28, 20, 20, 23, 34, 30, and 43. Obtain 95% confidence interval for population mean life of bulbs.

c)       A manufacturer claimed that at least 95% of the machine parts which is supplied to a factory confirmed to specification. An examination of a sample of 200 pieces such parts revealed that 18 were faulty.

i.           Is the manufacturer’s claim legitimate at 1% level of significance?

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6. a)       Before an increase in excise duty on coffee 800 out of a sample of 1000 persons were known to be taking coffee. After the increase in the duty 800 persons are now found to be taking coffee in a sample of 1200. Do you think that there has been a significant decrease in the consumption of coffee after the increase in the excise duty?  Test at 5% level of significance.

b)      Multiple myeloma, or blood plasma cancer, is characterized by increased blood vessel formulation (angiogenesis) in the bone marrow that is a predictive factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The following data represent the bone marrow microvessel density for patients who had a complete response to the stem cell transplant. The measurements were taken immediately prior to the stem cell transplant and at the time the complete response was determined:1

 Patients 1 2 3 4 5 6 7 Before 158 189 202 353 416 426 441 After 284 214 101 227 290 176 290

At the 0.05 level of significance, is there evidence that the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant?

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7. Write short notes on any two:

a)       Define quantitative and categorical variables with two examples of each

b)      Errors on hypothesis testing

c)       Sources of data

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