7. Consider this question stem for both the current question (7) and question eight (8): A sample of ten employees at an auditing firm is randomly selected. The probability that three employees in this sample have an honors' degree is 0.215 while the probability that four employees in this sample have an honors' degree is 0.251. Given that the probability of a success is p, determine the value of p approximate to three (3) decimal places. A. 0.084 B. 0.400 C. 0.854 D. 0.454 8. Using the information in question seven (7) and the result obtained thereby, determine the probability that at least two employees in this sample have an honors' degree. A. 0.549 B. 0.228 C. 0.495 D. 0.954 9. 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 10. Further to the information provided in question nine (9) 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 11. Further considering information given in questions nine (9) and ten (10), 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 12. Statistics show that only 25% of South African taxpayers submit their tax returns before the deadline date. Given a sample of six South African adults, what is the probability that exactly three have submitted their tax returns before the deadline date? A. 0.132 B. 0.453 C. 0.853 D. 0.343

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