1-) A quality control department noted took a sample of 40 product, and found the mean number of defect to be 6.15, with a standard deviation of 2.53 . The distribution was known to be normal.Construct a 95 percent confidence interval for the mean number of defects2-)A corporation is trying to estimate the mean amount an employees spends on dental care. They survey 45 employees, and find a mean amount spent of $1820, with a sample std dev of $660. Find a 95% confidence interval for the mean amount spent3-)Pepsi wants to estimate an average number of cans of Pepsi consumed. The sample 16 people and find the mean number of cans to be 60 with a sample standard deviation of cans of 20 a. Is the t or z distribution used here? Why?b. What is the value of the test statistic to be used for a 90% confidence interval?c. Create a 90% confidence interval.d. Could Pepsi be reasonable in concluding that the population mean is 59 cans?4-)Last year a survey showed that 30% of travelers stay in budget hotels. The hotel association wants to update this proportion. . a. The new study is to use the 90 percent confidence level. The estimate is to be within1 percent of the population proportion. What is the necessary sample size?b. If we wanted to reduce the required sample size, what could we do? 5-)A survey of singles was made regarding their restaurant eating habits. A sample of 60 singles had a sample mean number of restaurant visits was 2.76 meals per week. The std deviation of the sample was 0.75 meals per week. Create a 98 percent confidence interval for the mean of the population.