Question A - A company producing steel nails receives an order for 5000 nails of length 50 mm. Due to external factors such as temperature and pressure, the lengths of the nails produced by the machine is normally distributed with a standard deviation of 1.6 mm. Acceptable lengths (lengths that any customer will consent to buy) must have a tolerance of 2 mm. If the machine is set to produce nails with a mean length of 5.0 cm, determine the percentage of nails that are acceptable.
Question A - A company producing steel nails receives an order for 5000 nails of length 50 mm. Due to external
factors such as temperature and pressure, the lengths of the nails produced by the machine is normally
distributed with a standard deviation of 1.6 mm. Acceptable lengths (lengths that any customer will
consent to buy) must have a tolerance of 2 mm. If the machine is set to produce nails with a mean
length of 5.0 cm, determine the percentage of nails that are acceptable.
A. 0.7888 / B. 0.8877 / C. 0.9921 / D. 0.7878
Further to the information provided in question A above, we are informed that nails produced that
are shorter than the minimum acceptable length have to be scrapped. Consider that 4.8cm is still the
minimum threshold for acceptable nail length. If the cost to produce one nail is 45 cents, how much
does the company incur in Rand losses due to scrapping?
A. R247.70 / B. R347.91 / C. R237.60 / D. R471.99
Further considering information given in questions A and question B, if no more than 2% of nails are
to be scrapped, what should the new mean be set at in millimeters? Assume that the standard
deviation remains unchanged.
A. 51.28 / B. 52.21 / C. 68.92 / D. 69.28
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