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  • 10 Marks

QTB – Nov 2014 – L1 – SB – Q5a – Statistics

Calculate the Spearman's rank correlation coefficient between the scores in two subjects and interpret the result.

A business school preparing candidates for professional examinations conducted a mock examination to ascertain the level of preparedness of its candidates in two subjects: Quantitative Techniques in Business (QTB) and Management Information (MI). The table below gives the scores of twelve selected candidates.

Candidates 1 2 3 4 5 6 7 8 9 10 11 12
Score in QTB (x) 35 77 95 28 76 80 90 62 39 65 90 37
Score in MI (y) 50 82 89 58 65 61 84 59 48 53 80 52

Required:
i. Calculate the Spearman’s rank correlation coefficient between xx and yy. (9 Marks)
ii. Comment on the result in (i) above. (1 Mark)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q6a – Statistics

Calculate the monthly cost of replacing diodes based on failure probability and determine if a student can buy a gown based on expected money.

i. The laptops that are purchased by a company have 742 diodes with a life span of five months. These diodes fail on a regular basis according to the following probability distribution:

Life (months) 1 2 3 4 5
Probability of failure 0.10 0.30 0.35 0.20 0.05

If the cost of replacing a diode is ₦100, calculate the monthly cost of replacing the diodes as they fail. (4 Marks)

ii. Tadet, a student in the Accountancy Department of a Polytechnic, has the following chances of receiving money from her relatives:

  • 45% chance of receiving ₦5,000 from her sister,
  • 33% chance of receiving ₦8,000 from her brother,
  • 16% chance of receiving ₦11,000 from her aunt,
  • 6% chance of receiving ₦15,000 from her uncle.

Determine if Tadet will be able to buy a gown worth ₦8,000 from the money she is expecting from her relatives. (6 Marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q5b – Statistics

Calculate the Spearman's rank correlation coefficient between two accountants' rankings of ten banks.

Two Chartered Accountants: X and Y, were requested to rank ten banks A, B, C, D, E, F, G, H, I, J according to their performances during a financial year. X ranked the banks as follows:

  • X’s Rankings: E, B, G, A, C, D, H, F, J, I
  • Y’s Rankings: E, C, A, B, G, H, J, D, F, I

Calculate the Spearman’s rank correlation coefficient between X and Y and interpret your result.

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q4a – Statistics

Calculate the proportion of damaged blocks and the probability of taking a damaged block from a specific lorry using a tree diagram.

a. A fleet of lorries A, B, and C are loaded with blocks meant for a building site.
Lorry A carries 2/5 of all the needed blocks, B carries 3/4 of what lorry A carries, and lorry C carries the rest. Lorries A, B, and C contain 13%, 15%, and 11% damaged blocks, respectively.

By drawing a suitable tree diagram, calculate:
i. The proportion of damaged blocks in the fleet. (8 Marks)

ii. The probability of randomly taking a damaged block from lorry B. (2 Marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q2a – Statistics

Probability calculations for dice roll and random sampling in block production.

i. A six-sided and fair die is thrown into the air. What is the probability:

  • Of NOT getting a SIX?
  • That either a THREE, a FOUR, or a FIVE will fall uppermost?
  • Of obtaining an even number?
    (5 Marks)

ii. A block-making factory produces TWO types of blocks: 6-inch and 9-inch. ONE quarter of its output on a particular day are 6-inch blocks, while the remaining three-quarters are 9-inch blocks. If samples of 3 are taken at random, what is the probability of obtaining:

  • One 6-inch block?
  • Two 6-inch blocks?
  • One or two 6-inch blocks?
    (5 Marks)

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  • 1 Marks

QTB – May 2017 – L1 – SA – Q18 – Statistics

This question calculates the centered moving average for a specific year in a time series of cocoa production.

A ten-year record of cocoa production in a certain farm is tabulated as follows:

Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
Production (tonnes) 42 52 41 48 64 67 77 66 73 89

Based on a 4-year moving total, the centered moving average for the year 2007 is:
A. 79.5
B. 69.5
C. 59.5
D. 49.5
E. 39.5

 

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  • 1 Marks

QTB – May 2017 – L1 – SA – Q17 – Statistics

This question checks the range of values for the correlation coefficient r.

If is the correlation coefficient calculated for a bivariate data, then which one of the following is correct?

A. r=±
B. −1<r≤1
C. −1<r<1
D. −1≤r<1
E. −1≤r≤1

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  • 1 Marks

QTB – May 2017 – L1 – SA – Q16 – Statistics

This question asks to identify a false statement about normal distribution.

Which of the following is NOT TRUE about Normal Distribution?
A. Normal distribution is a frequency distribution.
B. Both tails of the distribution approach but never meet the horizontal axis.
C. It is a probability distribution of a continuous variable that fits many naturally occurring distributions.
D. The exact shape of the normal curve depends on the mean of the distribution.
E. The area under the normal curve represents the probability and totals 1 or 100%.

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  • 1 Marks

QTB – May 2017 – L1 – SA – Q15 – Statistics

This question involves calculating the probability that a defective item is from process B.

A large batch of components of TV sets is stocked by a company. The batch comprises components that are manufactured by processes A, B, and C. There are twice as many components from process A as from each of processes B and C in a batch. Components from A contain 8% defectives, and those from B and C contain 11% and 14% defectives respectively.
The probability that a defective item is from process B is:
A. 0.228
B. 0.238
C. 0.248
D. 0.258
E. 0.268

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  • 1 Marks

QTB – May 2017 – L1 – SA – Q14 – Statistics

This question involves identifying the estimable components of a time series.

The TWO components of a Time Series which are usually estimable are:
A. Trend and Cyclic variation
B. Seasonal variation and Trend
C. Random movements and Trend
D. Seasonal variation and Random movements
E. Cyclic variation and Seasonal variation

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  • 10 Marks

QTB – Nov 2014 – L1 – SB – Q5a – Statistics

Calculate the Spearman's rank correlation coefficient between the scores in two subjects and interpret the result.

A business school preparing candidates for professional examinations conducted a mock examination to ascertain the level of preparedness of its candidates in two subjects: Quantitative Techniques in Business (QTB) and Management Information (MI). The table below gives the scores of twelve selected candidates.

Candidates 1 2 3 4 5 6 7 8 9 10 11 12
Score in QTB (x) 35 77 95 28 76 80 90 62 39 65 90 37
Score in MI (y) 50 82 89 58 65 61 84 59 48 53 80 52

Required:
i. Calculate the Spearman’s rank correlation coefficient between xx and yy. (9 Marks)
ii. Comment on the result in (i) above. (1 Mark)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q6a – Statistics

Calculate the monthly cost of replacing diodes based on failure probability and determine if a student can buy a gown based on expected money.

i. The laptops that are purchased by a company have 742 diodes with a life span of five months. These diodes fail on a regular basis according to the following probability distribution:

Life (months) 1 2 3 4 5
Probability of failure 0.10 0.30 0.35 0.20 0.05

If the cost of replacing a diode is ₦100, calculate the monthly cost of replacing the diodes as they fail. (4 Marks)

ii. Tadet, a student in the Accountancy Department of a Polytechnic, has the following chances of receiving money from her relatives:

  • 45% chance of receiving ₦5,000 from her sister,
  • 33% chance of receiving ₦8,000 from her brother,
  • 16% chance of receiving ₦11,000 from her aunt,
  • 6% chance of receiving ₦15,000 from her uncle.

Determine if Tadet will be able to buy a gown worth ₦8,000 from the money she is expecting from her relatives. (6 Marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q5b – Statistics

Calculate the Spearman's rank correlation coefficient between two accountants' rankings of ten banks.

Two Chartered Accountants: X and Y, were requested to rank ten banks A, B, C, D, E, F, G, H, I, J according to their performances during a financial year. X ranked the banks as follows:

  • X’s Rankings: E, B, G, A, C, D, H, F, J, I
  • Y’s Rankings: E, C, A, B, G, H, J, D, F, I

Calculate the Spearman’s rank correlation coefficient between X and Y and interpret your result.

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q4a – Statistics

Calculate the proportion of damaged blocks and the probability of taking a damaged block from a specific lorry using a tree diagram.

a. A fleet of lorries A, B, and C are loaded with blocks meant for a building site.
Lorry A carries 2/5 of all the needed blocks, B carries 3/4 of what lorry A carries, and lorry C carries the rest. Lorries A, B, and C contain 13%, 15%, and 11% damaged blocks, respectively.

By drawing a suitable tree diagram, calculate:
i. The proportion of damaged blocks in the fleet. (8 Marks)

ii. The probability of randomly taking a damaged block from lorry B. (2 Marks)

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  • 10 Marks

QTB – May 2017 – L1 – SB – Q2a – Statistics

Probability calculations for dice roll and random sampling in block production.

i. A six-sided and fair die is thrown into the air. What is the probability:

  • Of NOT getting a SIX?
  • That either a THREE, a FOUR, or a FIVE will fall uppermost?
  • Of obtaining an even number?
    (5 Marks)

ii. A block-making factory produces TWO types of blocks: 6-inch and 9-inch. ONE quarter of its output on a particular day are 6-inch blocks, while the remaining three-quarters are 9-inch blocks. If samples of 3 are taken at random, what is the probability of obtaining:

  • One 6-inch block?
  • Two 6-inch blocks?
  • One or two 6-inch blocks?
    (5 Marks)

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  • 1 Marks

QTB – May 2017 – L1 – SA – Q18 – Statistics

This question calculates the centered moving average for a specific year in a time series of cocoa production.

A ten-year record of cocoa production in a certain farm is tabulated as follows:

Year 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
Production (tonnes) 42 52 41 48 64 67 77 66 73 89

Based on a 4-year moving total, the centered moving average for the year 2007 is:
A. 79.5
B. 69.5
C. 59.5
D. 49.5
E. 39.5

 

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  • 1 Marks

QTB – May 2017 – L1 – SA – Q17 – Statistics

This question checks the range of values for the correlation coefficient r.

If is the correlation coefficient calculated for a bivariate data, then which one of the following is correct?

A. r=±
B. −1<r≤1
C. −1<r<1
D. −1≤r<1
E. −1≤r≤1

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  • 1 Marks

QTB – May 2017 – L1 – SA – Q16 – Statistics

This question asks to identify a false statement about normal distribution.

Which of the following is NOT TRUE about Normal Distribution?
A. Normal distribution is a frequency distribution.
B. Both tails of the distribution approach but never meet the horizontal axis.
C. It is a probability distribution of a continuous variable that fits many naturally occurring distributions.
D. The exact shape of the normal curve depends on the mean of the distribution.
E. The area under the normal curve represents the probability and totals 1 or 100%.

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  • 1 Marks

QTB – May 2017 – L1 – SA – Q15 – Statistics

This question involves calculating the probability that a defective item is from process B.

A large batch of components of TV sets is stocked by a company. The batch comprises components that are manufactured by processes A, B, and C. There are twice as many components from process A as from each of processes B and C in a batch. Components from A contain 8% defectives, and those from B and C contain 11% and 14% defectives respectively.
The probability that a defective item is from process B is:
A. 0.228
B. 0.238
C. 0.248
D. 0.258
E. 0.268

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  • 1 Marks

QTB – May 2017 – L1 – SA – Q14 – Statistics

This question involves identifying the estimable components of a time series.

The TWO components of a Time Series which are usually estimable are:
A. Trend and Cyclic variation
B. Seasonal variation and Trend
C. Random movements and Trend
D. Seasonal variation and Random movements
E. Cyclic variation and Seasonal variation

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