i) The department of transport in Maseru is interested in collecting information about the average time spent by a motorist on the highway. An investigation carried out by the department claims that on average motorists spend 95 minutes on the highway. To test this claim, the Translux Company finds that from a random sample of 142 motorists the average time spent on the highway was 90.5 minutes. Assuming that time spent on the highway is normally distributed and the population standard deviation is 30 minutes, conduct a hypothesis test at the 5% significance level to support or refute the department of transport's claim. [10] ii) To cash in on the demand for Covid 19 vaccines, a pharmaceutical company is considering various options to improve its manufacturing process. Currently, running at full capacity, the business expects to make a net profit of USD 32 000. A business development firm has been hired to observe the manufacturing process and has listed the following possible improvements a. Continue to operate at the current capacity. b. Undertake an advanced level restructuring initiative that would cost USD 40 000. If successful, an increase in revenue of USD110 000 is expected. If unsuccessful an increase in revenue of USD 60 000 is expected. The probability of success is 0.8. c. Undertake a lower level restructuring initiative program costing USD 5000 which has a 50% chance of success. If successful, an increase in revenue of USD P70 000 is expected, and if unsuccessful an increase in revenue of USD 40 000 is expected. Present a decision tree and determine the most profitable course of action and comment on your findings [10] i) The department of transport in Maseru is interested in collecting information about the average time spent by a motorist on the highway. An investigation carried out by the department claims that on average motorists spend 95 minutes on the highway. To test this claim, the Translux Company finds that from a random sample of 142 motorists the average time spent on the highway was 90.5 minutes. Assuming that time spent on the highway is normally distributed and the population standard deviation is 30 minutes, conduct a hypothesis test at the 5% significance level to support or refute the department of transport's claim. [10] ii) To cash in on the demand for Covid 19 vaccines, a pharmaceutical company is considering various options to improve its manufacturing process. Currently, running at full capacity, the business expects to make a net profit of USD 32 000. A business development firm has been hired to observe the manufacturing process and has listed the following possible improvements a. Continue to operate at the current capacity. b. Undertake an advanced level restructuring initiative that would cost USD 40 000. If successful, an increase in revenue of USD110 000 is expected. If unsuccessful an increase in revenue of USD 60 000 is expected. The probability of success is 0.8. c. Undertake a lower level restructuring initiative program costing USD 5000 which has a 50% chance of success. If successful, an increase in revenue of USD P70 000 is expected, and if unsuccessful an increase in revenue of USD 40 000 is expected. Present a decision tree and determine the most profitable course of action and comment on your findings [10]