Suppose a standardized exam for admission to a special program has been passed by 54% of the students taking it over the last five years. Suppose that 1368 of 2400 students taking the test this year pass. What is the probability that at least 1368 would pass if the pass rate is 54%? Round your answer to four decimal places.
A)0.0017
B)0.9983
C)0.1072
D)0.2956
E)0.4000

Question

Suppose a standardized exam for admission to a special program has been passed by 54% of the students taking it over the last five years. Suppose that 1368 of 2400 students taking the test this year pass. What is the probability that at least 1368 would pass if the pass rate is 54%? Round your answer to four decimal places. ​
A)0.0017
B)0.9983
C)0.1072
D)0.2956
E)0.4000

Quizplus · Accepted Answer

Using a normal approximation to the binomial distribution, the probability of at least 1368 students passing can be calculated. The mean is 0.54 * 2400 = 1296, and the standard deviation is sqrt(2400 * 0.54 * 0.46) ≈ 24.49. The z-score for 1368 is (1368 - 1296) / 24.49 ≈ 2.94. The probability of a z-score of 2.94 or higher is approximately 0.0017.

Suppose a Standardized Exam for Admission to a Special Program