Question

Use the standard normal distribution or the t-distribution to construct a 90% confidence interval for the populationmean. Justify your decision. If neither distribution can be used, explain why Interpret the resultsIn a random sample of 50 people, the mean body mass index (BMI) was 26.9 and the standard deviation was 6.06.Which distribution should be used to construct the confidence interval? Choose the correct answer belowaO A. Use a t-distribution because the sample is random the population is normal, and o is unknownOB. Use a normal distribution because the sample is random, n 230, and o is knownO C. Use a t-distribution because the sample is random, n 230, and o is unknownOD. Use a normal distribution because the sample is random, the population is normal, and o is known.O E. Neither a normal distribution nor a t-distribution can be used because either the sample is not random, orn<30, and the population is not known to be normal

Answer 1

Use the standard normal distribution or the t-distribution to construct a 90% confidence interval for the population

From the observation, the distribution used to construct the confidence interval is

Therefore use a t - distribution because the sample is random and α is unknown

Hence the correct answer is Option C