Statistic Assignment. Title: Confidence Intervals 1.459 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 margin of error for the 95% confidence interval used to estimate the population proportion with n = 163 and x = 96.4. Construct the confidence interval for question 3.5. Interpret the confidence interval found in question 4.6. What are the requirements for a Student’s t-distribution?7. Find the critical value for tα/2 corresponding to n = 12 and 95% confidence level.8. Use the confidence level and sample data to find the margin of error E. College students’ annual earnings: 99% confidence, n = 81, = $3967, s = $8749. Construct the confidence interval for question 8 above.10. Interpret and describe the confidence obtained in question 9 in non-technical terms.