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. (4 marks)

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. (4 marks)

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. (4 marks)

A. 0.7888

B. 0.8877 C. 0.9921

D. 0.7878

i". 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. {4 marks) . 0.034 A 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. (4 marks) A. 0.549 . 0.228 B 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. It the machine is set to produce nails with a mean length of 5.0 cm, determine the percentage of nails that are acceptable. [4 marks) A. 07888 B. 0.887? C. 0.9921 D. 0.7878