BSC104C Engineering Mathematics Assignment

Assignment Help Engineering Mathematics

Reference no: EM132388252

BSC104C: Engineering Mathematics Assignment - Statistics and Standard Deviation

Bachelor of Science (Engineering) - Engineering Institute of Technology, EIT, Australia

Question 1: The diameters, in centimetres, of 60 holes bored in engine castings are measured and the results are as shown. Draw a histogram depicting these results and hence determine the mean, median and modal values of the distribution.

Diameters	2.011-2.014	2.016-2.019	2.021-2.024	2.026-2.029	2.031-2.034
Number of holes	7	16	23	9	5

Question 2: The tensile strength in megapascals for 15 samples of tin were determined and found to be:

34.61, 34.57, 34.40, 34.63, 34.63, 34.51, 34.49, 34.61, 34.52, 34.55, 34.58, 34.53, 34.44, 34.48 and 34.40

Calculate the mean and standard deviation from the mean for these 15 values, correct to 4 significant figures.

a) Calculate using the standard deviation formula (a table may help).

b) Check answer using calculator.

c) Check answer using a spreadsheet.

Part B -

Question 1: The mass in kilograms, correct to the nearest one-tenth of a kilogram, of 60 bars of metal are as shown.

Form a frequency distribution of about eight classes for these data. (You choose the classes)

Draw a histogram for the frequency distribution.

39.8, 40.3, 40.6, 40.0, 39.6, 39.6, 40.2, 40.3, 40.4, 39.8, 40.2, 40.3, 39.9, 39.9, 40.0, 40.1, 40.0, 40.1, 40.1, 40.2, 39.7, 40.4, 39.9, 40.1, 39.9, 39.5, 40.0, 39.8, 39.5, 39.9, 40.1, 40.0, 39.7, 40.4, 39.3, 40.7, 39.9, 40.2, 39.9, 40.0, 40.1, 39.7, 40.5, 40.5, 39.9, 40.8, 40.0, 40.2, 40.0, 39.9, 39.8, 39.7, 39.5, 40.1, 40.2, 40.6, 40.1, 39.7, 40.2, 40.3

Question 2: 500 tins of paint have a mean content of 1010 ml and the standard deviation of the contents is 8.7 ml. Assuming the volumes of the contents are normally distributed, calculate the number of tins likely to have contents whose volumes are less than

(a) 1025 ml

(b) 1000 ml and

Question 3: A sample of 2000 observations has a mean of 74 and a standard deviation of 12.

Using Chebyshev's theorem, find the minimum percentage of the observations that fall in the intervals

x^- ± 2s, x^- ± 2.5s, and x^- ± 3s.

Note that x^- ± 2s represents the interval x^- - 2s to x^- + 2s, and so on.

Also note that s is symbol for standard deviation in this example.

Question 4: Determine the coefficient of correlation for the data given, correct to 3 decimal places.

X	14	18	23	30	50
Y	900	1200	1600	2100	3800

Question 5: Determine the equation of the regression line of Y on X, correct to 3 significant figures.

X	6	3	9	15	2	14	21	13
Y	1.3	0.7	2.0	3.7	0.5	2.9	4.5	2.7

Reference no: EM132388252

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