Mubarak alnaimi
Task 1 – Learning Outcomes 4.1 and 4.2
Represent engineering data in tabular and graphical form
Determine measures of central tendency and dispersion

1. The masses of 50 castings were measured. The results in kilograms were as follows

4.6 4.7 4.5 4.6 4.7 4.4 4.8 4.3 4.2 4.8
4.7 4.5 4.7 4.4 4.5 4.5 4.6 4.4 4.6 4.6
4.8 4.3 4.8 4.5 4.5 4.6 4.6 4.7 4.6 4.7
4.4 4.6 4.5 4.4 4.3 4.7 4.7 4.6 4.6 4.8
4.9 4.4 4.5 4.7 4.4 4.5 4.9 4.7 4.5 4.6

a. Arrange the data in 8 equal classes between 4.2 and 4.9 kilograms.

b. Determine the frequency distribution.

c. Draw the frequency histogram and frequency polygon.

d. Calculate the mean, median and interquartile range.

e. Calculate the standard deviation for the data. You may wish to use a coded method.

f. Calculate the limits within which you would expect (i) 95% and (ii) 99% of components to fall.
Task 2 – Learning Outcomes 4.3
Apply linear regression and product moment correlation to a variety of engineering situations
2. Following the machining process the components are to be hardened and then tempered. As part of the design process a sample of eight components was tempered at different temperatures with the following results:

Temperature °C Hardness Vpn
240 550
275 532
300 525
335 514
360 474
395 470
420 458
455 446

a. Draw a scatter diagram of this data and calculate the correlation coefficient. Comment on the nature of the relationship between temperature and hardness.

b. Use least-squares linear regression analysis to establish an equation with which hardness can be predicted from temperature for this particular steel.

c. Use the equation found above to estimate the hardness values for temperatures of 260°C and 370°C.

d. Comment on the accuracy and reliability of estimates that may be obtained using the preceding analysis.

Task 3 – Learning Outcome 4.4
Use the normal distribution and confidence intervals for estimating reliability and quality of engineering components and systems
3. A machine produces components whose diameters should be distributed Normally with mean 0.15 cm and Standard Deviation 0.01 cm. It is suspected that the mean may have changed over a long period of use.

To test for this possibility, a sample of 150 components is drawn and the mean is computed at 0.147. Using the assumption that µ is true, determine whether there is any evidence at the 5% level that the mean of the components has changed.

 
4. The blanks are to be machined to the component profile. The machining equipment can only accept blanks which are no more than 120mm wide and 500mm long.

The probability of the length being greater than 500mm is 2.5% (0.025) and the probability of the width being greater than 120mm is 3% (0.03).

a. Calculate the probability of a blank being oversize in both dimensions.

b. Show that the probability that a blank is unacceptable (i.e. is oversize in either dimension) is 0.05425.

c. Use the binomial distribution to find the probability that two blanks selected at random from a sample of six will be oversize, if the probability of a blank being oversize in either dimension is 0.05425.

d. Use the Poisson distribution to find the probability that two blanks selected at random from a box of 20 will be oversize, using p = 0.05425 as above.