ENGR 102-Identify the categories that make up 75 $ of the cases

1-Identify the categories that make up 75 $ of the cases of failure so that you can advise the manufacturing company where to concentrate their efforts to improve. in other words wat are the specific categories that account for 75% of the failure ? (10 pts) Fill in the blanks: The number of hours it takes for a certain metal part to wear out is assumed to be from a population with a normal probability distribution with a mean of 1,100 hours and a standard deviation of 83 hours. If this is true, then approximately 68 percent of the parts are predicted to wear out between ________ and ________ hours of operation.5. (20 pts) Suppose that the scores on a mathematics aptitude test are normally distributed. If the test results have a mean score of 84 points and a standard deviation of 10.2 points, what is the probability that a student from this population scored 89 points or lower on this particular test? (Hint: first compute the Z-score.)6. (20 pts) The lifespan of an electrical component is assumed to be normally distributed with an average life of 10 years and a standard deviation of 2 years. The electrical component manufacturer wants to offer their customers a product-replacement guarantee, but hopes to replace at most only 12.3% of the components due to failure. How long of a replacement guarantee period should the manufacturer offer to buyers of this part?(This one’s a bit tougher. Partial credit is certainly possible. Hint: you will need to use the Z-score table again.)