Name:______________________________________Module 2 Homework Assignment1.) 459 randomly selected light bulbs were tested in a laboratory, 291 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.2.) Find the critical value for zα/2 that corresponds to a degree of confidence of 98%.3.) Find the critical value for tα/2 corresponding to n = 12 and 95% confidence level.4.) Use the confidence level and sample data to find the margin of error E. College students’ annual earnings: 99% confidence, n = 74, = $3967, s = $874 5.) Construct the confidence interval for question 4 above.6.) Write a statement that correctly interprets the confidence interval found in question 5.7.) Find the critical value corresponding to a sample size of 19 and a confidence level of 99% if the test is two-tailed.8.) Find the critical value corresponding to a sample size of 19 and a confidence level of 99% if the test is two-tailed. 9.) The values listed below are the waiting times (in minutes) of customers at the Bank of Providence, where customers enter any one of three different lines that have formed at three teller windows. Construct a 95% confidence interval for the population standard deviation and write a statement that correctly interprets the results.4.2 5.4 5.8 6.2 6.7 7.7 8.5 9.3 10.010.)You want to estimate s for the population of waiting times at a fast-food restaurant’s drive-up windows, and you want to be 95% confident that the sample standard deviation is within 20% of s. Find the minimum sample size needed. Is this sample size practical?