A random sample of n measurements was selected from a population with unknown mean μ and standard deviation o= 15 for ea

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A random sample of n measurements was selected from a population with unknown mean μ and standard deviation o= 15 for each of the situations in parts a through d. Calculate a 90% confidence interval for μ for each of these situations. a. n = 50, x = 36 b. n = 200, x= 114 c. n = 80, x= 14 d. n = 80, x = 4.27 e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a through d? Explain. a. (Round to two decimal places as needed.) b. (Round to two decimal places as needed.) C. (Round to two decimal places as needed.) d. (Round to two decimal places as needed.) e. Choose the correct answer below. O A. No, since the confidence level is at least 90%, the underlying distribution need not be normal. O B. No, since the sample sizes are large (n ≥30) and randomly selected from the target population, the condition guarantees that the sampling distribution of x is approximately normal. O C. No, since the sample sizes are large (n ≥30), the condition guarantees that the sampling distribution of x is approximately normal. O D. No, since the sample was randomly selected from the target population, the sampling distribution of x is guaranteed to be approximately normal. O E. Yes, the underlying distribution must be normal for the validity of these confidence intervals