for option (d) first blank options are: a decrease/an increase. second blank options are: sample mean/critical value/sample size/standard deviation, third blank options are: decrease/not change/increase A random sample of 100 observations from a normally distributed population possesses a mean equal to 92.7 and a standard deviation equal to 5.9. Use this information to complete parts a through e below.a. Find a 95% confidence interval for µ.(Round to two decimal places as needed.)b. What do you mean when you say that a confidence coefficient is 0.95?O A. A confidence coefficient of 0.95 means that there is a probability of 0.95 that an interval estimator constructed using this coefficient will enclose the population parameter.B. A confidence coefficient of 0.95 means that there is a probability of 0.95 that an interval estimator constructed using this coefficient will contain all of the values in the relevant sample.O C. A confidence coefficient of 0.95 means that 95% of the values in the population will be contained in an interval estimator constructed using this coefficient.D. A confidence coefficient of 0.95 means that 95% of the values in any sample taken from the population will be contained in an interval estimator constructed using this coefficient.c. Find a 99% confidence interval for µ.(Round to two decimal places as needed.)d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?Increasing the confidence coefficient while keeping the sample size fixed will causein theThis means that the width of the confidence interval wille. Would your confidence intervals of parts a and c be valid if the distribution of the original population were not normal? Explain.O A. Yes, since the sample sizes are large (n > 30), the condition guarantees that the sampling distribution of x is approximately normal.B. Yes, since the sample was randomly selected from the target population, the sampling distribution of x is guaranteed to be approximately normal.C. No, the underlying distribution must be normal for the validity of these confidence intervalsD. Yes, since the confidence level is at least 90%, the underlying distribution need not be normal.O E. Yes, since the sample sizes are large (n2 30) and randomly selected from the target population, the condition guarantees that the sampling distribution of x is approximately normal.

Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for you. To get remaining sub-part solved please repost the complete question and mention the sub-parts to be solved. a)At 95% confidence level, the value of z is 1.96. Then, the confidence interval isx±zsn=92.7±1.965.9100=92.7±1.965.910=92.7±1.960.59=92.7±1.16=91.54 , 93.86b)The option A is correct.c) At 99% confidence level, the value of z is 2.58. Then, the confidence interval isx±zsn=92.7±2.585.9100=92.7±2.585.910=92.7±2.580.59=92.7±1.52=91.18 , 94.22