<p>BUSINESS STATISTICS SPRING 2003 </p><p>Tutorial 6</p><p>Week beginning: 8 September 2003 Due date: 7 October 2003 Value: Tutorials 4 - 6 consolidate the unit of work on Probability and Probability distributions. These three tutorials combined represent 10% of the overall assessment. Marking criteria: Marks will be awarded for:  the correct answers;  appropriate detailed working;  appropriate diagrams;  clear and valid explanations where appropriate.</p><p>In this tutorial you will consolidate the work done in lectures on the normal distribution. Work can be handwritten as long as it is neatly and clearly presented with the usual cover sheet.</p><p>1. Given that Z is the standard normal random variable, find the following probabilities.</p><p> a. P(0＃ Z 1.96) b. P( Z < 1.09) c. P(- 2.42 < Z < - 0.53) d. P( Z 0.36) e. P(- 1.07＃ Z 3.35)</p><p>2. Use the standard normal tables to find the values for z* , for which</p><p> a. P( Z� z* ) 0.0150</p><p> b. P( Z< z* ) = 0.20</p><p> c. P(- z*＃ Z z * ) = 0.90</p><p>3. The lengths of the long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes.</p><p> a. What is the probability that a long-distance call lasts between 5 and 10 minutes? b. What is the probability that a long-distance call lasts more than 12 minutes? c. What is the probability that a long-distance call lasts less than 8 minutes?</p><p>4. A company that manufactures tyres find that their tyres last distances that are normally distributed with a mean of 57500 kilometers and a standard deviation of 7000 kilometers.</p><p> a. What is the probability that a tyre will last a distance of at least 50000 kilometers? b. What is the probability that a tyre will last a distance of more than 55000 kilometers but less than 65000 kilometers? c. The manufacturer wants to guarantee the tyres so that only 3% will be replaced because of failure before the guaranteed number of kilometers. For how many kilometers should the tyres be guaranteed?</p><p>Work to be completed and handed in by 5pm, 7 October 2003, in the assignment box in Building 1. Questions may be neatly handwritten showing appropriate working. Each tutorial must have a cover sheet showing your name, student number, tutorial day and time, and tutorial number ie Tutorial 6. All three tutorials should be bundled together unless you choose to submit each separately, as completed.</p>