11. The time taken to assemble a car in a certain plant is a random variable having a normal distribution with ahours and a standard deviation of 2 hours. What is the probability that a car can be assembled at this plant in time

12. A radar unit is used to measure speeds of cars on a motorway. From past testing, the speeds are assumed distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. a. Assuming the speeds have not changed, what is the probability that a car picked at random is travelling at more than 100 km/hr?b. Assuming the speeds have not changed, what is the probability that a car picked at random is travelling at more than 110 km/hr?c. If a randomly selected car is found to be driving at 132 km/hr, what might be concluded? Explain and justify your answer.

13. Entry to a certain University is determined by a national test. The scores on this test are normally distributemean of 500 and a standard deviation of 100. Tom wants to be admitted to this university and he knows that hbetter than at least 70% of the students who took the test. Tom takes the test and scores 585. Will he be admiuniversity? Explain your answer.

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Chapter 5 / Exercise 28

**Mathematical Applications for the Management, Life, and Social Sciences**

Harshbarger

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14. For a certain type of computers, the length of time between charges of the battery is normally distributed with a mean of 50 hours and a standard deviation of 15 hours. John owns one of these computers and wants to know the probability that the length of time will be between 50 and 70 hours.15. The lengths of similar components produced by a company are approximated by a normal distribution modmean of 5 cm and a standard deviation of 0.02 cm.a. If a component is chosen at random, what is the probability that the length of this component is between 4.98 and 5.02 cm?b.If a component is chosen at random, what is the probability that the length of this component is between 4.96 and 5.04 cm?c. If a component is chosen at random and its length is found not to be between 4.96 and 5.04the company be concerned? Explain and justify your answer.