It is known that the scores of an exam vary in a certain population with values according to a normal distribution of unknown mean and standard deviation. In a sample of 13 notes from this population, the following results were obtained: 54 63 61 63 63 59 63 61 60 57 55 62 58 a. Considering the 92% two-sided confidence interval for the mean exam score of a certain population, what is the lower bound of this interval?  b. Considering the 92% two-sided confidence interval for the mean exam score of a certain population, what is the upper limit of this interval?  c. With the information obtained in this sample, calculate what would be the margin of error of a 99.9% confidence interval for the mean score in the exam of a certain population.

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It is known that the scores of an exam vary in a certain population with values according to a normal distribution of unknown mean and standard deviation. In a sample of 13 notes from this population, the following results were obtained:

54 63 61 63 63 59 63 61 60 57 55 62 58

a. Considering the 92% two-sided confidence interval for the mean exam score of a certain population, what is the lower bound of this interval? 
b. Considering the 92% two-sided confidence interval for the mean exam score of a certain population, what is the upper limit of this interval? 
c. With the information obtained in this sample, calculate what would be the margin of error of a 99.9% confidence interval for the mean score in the exam of a certain population. 

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