## Description

BCS-040 Solved Assignment For IGNOU BCA 4th Semester. This solution is valid for July 2018 and January 2019 session.

**Course Code : BCS-040**

**Course Title : Statistical Techniques**

**Assignment Number : BCA(4)040/Assignment/2018-19**

**Maximum Marks : 100**

**Weightage : 25%**

**Last Date of Submission : 15th October, 2018 (For July, 2018 Session)**

**15th April, 2019 (For January, 2019 Session)**

*Note: This assignment has 10 questions of 80 marks (each question carries equal marks). Answer all the questions. Rest 20 marks are for viva voce. You may use illustrations and diagrams to enhance explanations. Please go through the guidelines regarding assignments given in the Programme Guide for the format of presentation.*

**Question 1:** Given the following sample of 20 numbers: (10 marks)

12 41 48 58 14 43 50 59 15 45 52 72 18 45 54 78 41 47 56 79

(a) Compute mean, variance and standard deviation.

(b) If the largest value in the above set of numbers is changed to 500, to what extent are the mean and variance affected by the change? Justify your answer.

**Question 2:** What are the various probability distributions, give respective formulas of each type of distribution. Now Solve the problem “The probability that at least one of the two independent events occurs is 0.5. Probability that the first event occurs but not the second is 3/25. Also the probability that the second event occurs but not the first is 8/25.”Find the probability that none of the two events occurs. (10 marks)

**Question 3:** Which Probability distribution is applicable to the situation given below, give reasons in support of our response.

“Calls at a telephone switchboard occur at an average rate of 6 calls per 10 minutes. Suppose the operator leaves for a 5-minute coffee break”. What is the probability that exactly two calls occur while the operator is away? (10 marks)

**Question 4:** A Statistics professor has given five tests. A student scored 70, 75, 65, 80 and 95 respectively in the five tests. The professor decides to determine his grade by randomly selecting a sample of 3 test scores. Construct the sampling distribution for this process. (10 marks)

**Question 5:** Two new types of petrol, called premium and super, are introduced in the market, and their manufacturers claim that they give extra mileage. Following data were obtained on extra mileage which is defined as actual mileage minus 10. (10 marks)

Ordinary Petrol | 1 | 2 | 2 | 1 |

Premium Petrol | 2 | 2 | 1 | 3 |

Super Petrol | 4 | 1 | 2 | 3 |

(i) Using ANOVA, test whether premium or super gives an extra mileage.

(ii) What is your estimate for the error variance?

(iii) Assuming that the error variance is known and is equal to 1, obtain the 95 % confidence interval for the mean extra mileage of super.

**Question 6:** Following data are given for marks in subject A and B in a certain examination : (10 marks)

SUBJECT A | SUBJECT B | |
---|---|---|

MEAN MARKS | 36 | 85 |

STANDARD DEVIATION | 11 | 8 |

Coefficient of correlation between A and B = ±0.66

i) Determine the two equations of regression

ii) Calculate the expected marks in A corresponding to 75 marks obtained in B.

**Question7:** A drilling machine bores holes with a mean deviation of 0.5230 cm and a standard deviation of 0.0032 cm. Calculate 2-sigma and 3-sigma upper and lower control limits for means of samples 4 and prepare a control chart. (10 marks)

**Question 8: **Construct 5- yearly moving averages from the following data (10 marks)

Year | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | 2011 | 2012 |

Sale | 105 | 107 | 109 | 112 | 114 | 116 | 118 | 121 | 123 | 124 | 125 | 127 | 129 |

**Question 9:** Which Probability distribution is applicable to the situation given below, give reasons in support of our response.

In 120 throws of a single dice, following distribution of faces was observed. (10 marks)

FACES | 1 | 2 | 3 | 4 | 5 | 6 | TOTAL |

F0 | 30 | 25 | 18 | 10 | 22 | 15 | 120 |

From the given data, verify that the hypothesis “dice is biased” is acceptable or not.

**Question 10:** Explain the following. (10 marks)

(a) t – Test

(b) CHI – SQUARE distribution

(c) Linear systematic sampling

(d) Circular systematic sampling

(e) Z-Test

(f) Goodness of Fit Test

(g) Time series Analysis

(h) Forecasting

(i) Regression analysis

(j) Correlation coefficient

**Please note: Part (iii) of question 5 is not answered in this solution.**

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