1. (12 points ) A very large batch component has arrived at a distributor. 10% of the components in the batch are defective but the distributor does not know the exact percentage of the defective components .He decides to randomly select 10 components and to accept the batch only if the number of defective components in the sample is at most 2. a. What is the probability that the batch will be accepted ? b. What is the probability that among 10 components .5 of them are defective ? c. What is the probability that among 10 components , 3 or 4 of them are defective ? 2. (8 points ) Time that is needed to fix a car engine problem follows a normal distribution with mean of 48 and std of 5 minutes .A mechanics tells a customer that it takes maximum of 1 hour to fix the engine . a. What is the probability that the mechanic's estimation about the time does not happen ? b. If the mechanic wants to give an estimation about time with 98% confidence ,what wouid be the time ? 3. (6 points )On a given test with a maximum possible score of 100 points , the vast majority of the 259 students in a class scored either a perfect score or a zero , with only one student scoring within 10 points of the mean .Could we say that the test scores are normally distributed? Explain your answer. 4. (8 points )A random sample consisting of 200 business executives working in the Downtown area of Vancouver is drawn and they were asked to answer a set of questions . One question in the survey asked about their annual salary and another about their annual expenses on luxury goods. We regress the spending on salary, and the regression has R2 = 0.884 . a. Interpret the result of the R2 value in this context b. Based on the R2 information , could we infer that higher income is associated with a higher flower expenses of luxury goods ? Explain your answer 5. (9 points )The following regression model shows the relationship between selling price of a house [y] and the number of bedrooms [x]; y =100 +0.6 x. Another separate regression model shows the relationship between selling price of house [y] and the Eevel of the crime per week in the neighborhood [x]; y =100 -0.3 x. a. Draw the regression line for the first and second regression b. Write an interpretation for the slope coefficient in the first and second regression. Be specific c. What is the estimated value of the price of a house which has two bedrooms ? 6. (5 points )Given certain level of significance ,what is the relationship between the confidence interval and size of the sample ? Explain your answer . 7. (12 points ) In a sample of 100 wine consumers , 20 thoughts that screw tops were an acceptable substitute for natural corks.Suppose a particular winery decided