A University Director of Studies records the number of students failing the examinations of several courses. The data are presented in the following stem and leaf plot where the stems are with units 10 and the leaves are with units 1. Page 3 of 4 0| 224 0| 59 1| 59 1| 57889 2| 2| 3| 144 3| 5 (i) Determine the range of the data (ii) Determine the median number of students failing the examinations of these courses. (iii) Determine the mean number of students failing the examinations of these courses. B. A manufacturing company is analyzing its accident record. The accidents fall into two categories: Minor—dealt with by first aider: Average cost k50 Major—hospital required. Average cost k1,000 The company has 1,000 employees, of which 180 are office staff and the rest work in the factory. The analysis shows that 10% of employees have an accident each year and 20% of accidents are major. It is assumed that an employee has more than one accident in a year. (i) Determine the expected total cost of accidents in a year. On further analysis it is discovered that a member of office staff has half the probability of having an accident relative those in the factory. (ii) Show that the probability that a given a member of office staff has an accident in a year is 0.0549. (iii) Determine the probability that a randomly chosen employee who has had an accident is office staff. C. An insurance company calculates car insurance company calculates car insurance premiums based on the age of the policyholder according to three age Page 4 of 4 groups: Group A consists of drivers younger than 22 years old; Group B consists of drivers 22—33 years old, and Group C consists of drivers older than 33 years. Its portfolio consists of 10% Group A policyholders, 38% Group B policyholders and 52% Group C policyholders. The probability of a claim in any 12 month period for a policy belonging to Group A, B or C is 13%, 3% and 2%, respectively. (i) Calculate the probability that a randomly chosen policy holder from this portfolio will make a claim during a 12 month period. One of the company’s policyholders has just made a claim (ii) Calculate the probability that the policy holder is younger than 22 years. D. An airline is analyzing the punctuality of its scheduled flights. It measures departures and arrivals and classifies them as early, on time or late. From its records, no flights depart early and 85% depart on time. Arrivals are early 10% of the time and late 20% of the time. (i) Determine the probability that a flight arrives on time Further explanation shows that None of the flights that depart late are early arrivals. 10% of the flights that depart on time are late arrivals. (ii) Determine the probability that a flight will arrive early if its departure is on time. (iii) Show that the probability that a flight both departs on time and arrives on time is 0.665. (iv) Determine the probability that a flight will arrive on time if it departs late. (v) Determine the probability that if a flight arrives late it departed on time.
A University Director of Studies records the number of students failing the examinations of several courses. The data are presented in the following stem and leaf plot where the stems are with units 10 and the leaves are with units 1.
Page 3 of 4
0| 224
0| 59
1| 59
1| 57889
2|
2|
3| 144
3| 5
(i) Determine the
(ii) Determine the
(iii) Determine the mean number of students failing the examinations of these courses.
B. A manufacturing company is analyzing its accident record. The accidents fall into two categories:
Minor—dealt with by first aider: Average cost k50
Major—hospital required. Average cost k1,000
The company has 1,000 employees, of which 180 are office staff and the rest work in the factory.
The analysis shows that 10% of employees have an accident each year and 20% of accidents are major. It is assumed that an employee has more than one accident in a year.
(i) Determine the expected total cost of accidents in a year.
On further analysis it is discovered that a member of office staff has half the probability of having an accident relative those in the factory.
(ii) Show that the probability that a given a member of office staff has an accident in a year is 0.0549.
(iii) Determine the probability that a randomly chosen employee who has had an accident is office staff.
C. An insurance company calculates car insurance company calculates car insurance premiums based on the age of the policyholder according to three age
Page 4 of 4
groups: Group A consists of drivers younger than 22 years old; Group B consists of drivers 22—33 years old, and Group C consists of drivers older than 33 years.
Its portfolio consists of 10% Group A policyholders, 38% Group B policyholders and 52% Group C policyholders.
The probability of a claim in any 12 month period for a policy belonging to Group A, B or C is 13%, 3% and 2%, respectively.
(i) Calculate the probability that a randomly chosen policy holder from this portfolio will make a claim during a 12 month period.
One of the company’s policyholders has just made a claim
(ii) Calculate the probability that the policy holder is younger than 22 years.
D. An airline is analyzing the punctuality of its scheduled flights. It measures departures and arrivals and classifies them as early, on time or late. From its records, no flights depart early and 85% depart on time. Arrivals are early 10% of the time and late 20% of the time.
(i) Determine the probability that a flight arrives on time
Further explanation shows that
None of the flights that depart late are early arrivals.
10% of the flights that depart on time are late arrivals.
(ii) Determine the probability that a flight will arrive early if its departure is on time.
(iii) Show that the probability that a flight both departs on time and arrives on time is 0.665.
(iv) Determine the probability that a flight will arrive on time if it departs late.
(v) Determine the probability that if a flight arrives late it departed on time.
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