MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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PS 3 Correct to the nearest 0.1 kg, the masses of five people in a fitness class are 70.8, 68.7, 73.2, 79.7 and 82.6 kg. a Find the mean mass. Explain briefly why your answer is an estimate. b Calculate an estimate of the standard deviation of the masses. 4 An employee paints a design on plates in a factory. At the end of each day the plates are inspected and some are rejected. The table shows the number of plates rejected over a period of 30 days. No. rejects No. days 8 No. female relatives No. children (f) 0 18 Circumference (c metres) Show that the standard deviation of the daily number of rejects is approximately equal to one-quarter of the range. 5 Fifty children were asked how many female relatives they have. The table shows that the children said they have 3, 4, 6 or r female relatives. 3 No. oil drums (f) 14 1 5 b 2 3 1.84 <c< 1.94 200 4 244-246 10 3 1 22 a Find the value of r, given that the mean number of female relatives is exactly 4.64. b Use your answer to part a to find the variance, correct to 2 decimal places. 6 Six wind turbines are to be erected in a straight line across the fields of a farm. The wind turbine closest to the farmhouse, which will be in-line with the turbines, will be erected 200 metres away, and there will be exactly 250 metres between one turbine and the next. Find the mean and standard deviation of the distances from the turbines to the farmhouse. 7 The circumferences, c metres, of 400 cylindrical oil drums are summarised in the following table. 4 1 1.94 < c < 2.16 130 6 250-252 24 5 1 8 16-20 21-25 26-30 31-35 5 12 18 14 6 1 r 6 a Write down a suitable value that can be used to represent the circumference of the oil drums in each class. Use your values from part a to calculate an estimate of: i the mean circumference ii the variance of the circumferences. The mass of coffee in each of 80 packets of a certain brand was measured, correct to the nearest gram. The results are shown in the table. 247-249 Mass (grams) No. packets 20 253-255 18 70 2.16 ≤ c < 2.66 256-258 8 a Estimate the mean and standard deviation of the masses, setting out your work in a table. b State two ways in which the accuracy of these estimates could be improved. 9 The ages, in completed years, of the 104 workers in a company are summarised as follows. Age (years) Frequency a Estimate the mean and standard deviation of the workers' ages. b In another company, with a similar number of workers, the mean age is 28.4 years and the standard deviation is 9.9 years. Briefly compare the age distribution in the two companies. 36-40 41-50 51-60 61-70 6 25 16 8 10 The diagram shows a cumulative frequency graph for the lengths of telephone calls from a house during the first six months of last year.
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Transcribed Image Text:PS 3 Correct to the nearest 0.1 kg, the masses of five people in a fitness class are 70.8, 68.7, 73.2, 79.7 and 82.6 kg. a Find the mean mass. Explain briefly why your answer is an estimate. b Calculate an estimate of the standard deviation of the masses. 4 An employee paints a design on plates in a factory. At the end of each day the plates are inspected and some are rejected. The table shows the number of plates rejected over a period of 30 days. No. rejects No. days 8 No. female relatives No. children (f) 0 18 Circumference (c metres) Show that the standard deviation of the daily number of rejects is approximately equal to one-quarter of the range. 5 Fifty children were asked how many female relatives they have. The table shows that the children said they have 3, 4, 6 or r female relatives. 3 No. oil drums (f) 14 1 5 b 2 3 1.84 <c< 1.94 200 4 244-246 10 3 1 22 a Find the value of r, given that the mean number of female relatives is exactly 4.64. b Use your answer to part a to find the variance, correct to 2 decimal places. 6 Six wind turbines are to be erected in a straight line across the fields of a farm. The wind turbine closest to the farmhouse, which will be in-line with the turbines, will be erected 200 metres away, and there will be exactly 250 metres between one turbine and the next. Find the mean and standard deviation of the distances from the turbines to the farmhouse. 7 The circumferences, c metres, of 400 cylindrical oil drums are summarised in the following table. 4 1 1.94 < c < 2.16 130 6 250-252 24 5 1 8 16-20 21-25 26-30 31-35 5 12 18 14 6 1 r 6 a Write down a suitable value that can be used to represent the circumference of the oil drums in each class. Use your values from part a to calculate an estimate of: i the mean circumference ii the variance of the circumferences. The mass of coffee in each of 80 packets of a certain brand was measured, correct to the nearest gram. The results are shown in the table. 247-249 Mass (grams) No. packets 20 253-255 18 70 2.16 ≤ c < 2.66 256-258 8 a Estimate the mean and standard deviation of the masses, setting out your work in a table. b State two ways in which the accuracy of these estimates could be improved. 9 The ages, in completed years, of the 104 workers in a company are summarised as follows. Age (years) Frequency a Estimate the mean and standard deviation of the workers' ages. b In another company, with a similar number of workers, the mean age is 28.4 years and the standard deviation is 9.9 years. Briefly compare the age distribution in the two companies. 36-40 41-50 51-60 61-70 6 25 16 8 10 The diagram shows a cumulative frequency graph for the lengths of telephone calls from a house during the first six months of last year.
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