Answer to Question #257375 in Statistics and Probability for Mumba

Question

The marks of 500 candidates in an examination are normally distributed with a mean of 45 marks and a standard deviation of 20 marks. Given that the pass marks is 41, estimate the of candidates, who passed the examination

Answer 1

$\mu=45 \\ \sigma=20 \\ P(X>41) = 1 -P(X<41) \\ = 1 -P(Z < \frac{41-45}{20}) \\ = 1 -P(Z< -0.2) \\ = 1 -0.4207 \\ = 0.5793$

Candidates, who passed the examination $= 500 \times 0.5793 = 289.65 ≈ 290$