me with these questions 1. A car dealership claims that its technicians can diagnose the fault in the motor vehicles within an average of 42 minutes. A customer does not believe the car dealership's claim and thinks it will take longer than 42 minutes to diagnose the fault in a motor vehicle. In order to test the claim, the customer randomly selects 58 clients who visit the dealership and finds that the average diagnostic time is 44.6 minutes. Assuming that the population standard deviation of 8.6 minutes and the diagnostic time is close to normal distribution. 2. Test the customer's claim that the car dealership takes on average longer than 42 minutes to diagnose the fault in a motor vehicle with a 1% level of significance Critical value z = 2.327 3. The CEO of a large electric utility company claims that 80 percent of his 1,000,000 customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 100 customers, using simple random sampling. Among the sampled customers, 73 percent say they are very satisfied. Based on these findings, can we reject the CEO's hypothesis that 80% of the customers are very satisfied? Use a 0.05 level of significance. Follow the steps outlined in 1.1 up to 1.4. 1.1. Set up the hypothesis to be tested (2) 1.2. State the decision rule (Use critical value Z = 1.96) (2) 1.3. Calculate the test statistic (2) 1.4. Conclude on whether 80 percent of the company's customers are very satisfied with the company's service. (1) 4. A survey of 500 males and female respondents was conducted about the ownership of Zenith Mobile products. Each respondent was asked if they owned a Zenith Mobile product. Of the 220 males respondents, 56 answered "yes". Of the 280 female respondents, 65 answered "yes". Calculate at the 10% level of significance if male respondents are more likely to own a Zenith Mobile product than female respondents z-crit = 1.282 5. A store owner observed a random sample of 240 customers and found that 86 customers used debit cared to pay while the remainder used cash. Construct a 95% confidence interval (CI) for the actual proportion of customers who pay for cash for their purchases. z-crit = 1.96 6. Juice bottles are advertised to contain 0.75L pure juice. A random sample of 15 bottles found that the average fill was 0.745L with a variance of 0.0027L. Assume that the fill of 0.75L juice bottles is normally distributed. Using a 99% confidence level, estimate the actual mean fill of all 0.75L juice bottles t = 2.947 7. A company sells cellphones to customers. It found that, on average, 5 units are sold per hour. What is the probability that on a given hour no less than 2 units are sold? 2 What is the probability that only 5 units are sold in a 2-hour period? 8. A cellphone store sells cellphone batteries. The battery experiences an overheating problem and the problem follows a Poisson process. The problem occurs, on average, 3 times a given week. 1) What is the probability that the overheating problem will occur no less than 2 times in a given 2 weeks? 2) What is the chance that the overheating problem will occur once a day in a given 3 weeks