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Answer:
The 95% confidence interval for the proportion of students that obtain a letter grade of B or better from this professor is (0.2056, 0.3544). The interpretation is that we are 95% sure that the true proportion of students who obtain a letter grade of B or better from this professor is between 0.2056 and 0.3544.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
For this problem, we have that:
140 students, so
B or better are grades of A or B.
5% earn As, 23% earn Bs, so
95% confidence level
So , z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 95% confidence interval for the proportion of students that obtain a letter grade of B or better from this professor is (0.2056, 0.3544). The interpretation is that we are 95% sure that the true proportion of students who obtain a letter grade of B or better from this professor is between 0.2056 and 0.3544.