Scores on a test are normally distributed with a mean of 68.2 and a standard deviation of 10.4. Estimate the probability that among 75 randomly selected students, at least 20 of them score greater than 78.
A)0.0239
B)0.0166
C)0.0113
D)0.1736

Question

Quizplus · Accepted Answer

The probability that a randomly selected student scores greater than 78 is P(X > 78) = P(Z > (78 - 68.2) / 10.4) = P(Z > 0.942) = 0.1736. The probability that at least 20 of 75 randomly selected students score greater than 78 is 1 - P(X ≤ 19) = 1 - binomcdf(75, 0.1736, 19) = 0.0239.

Scores on a Test Are Normally Distributed with a Mean