The marks of 500 candidates in an examination are normally distributed with a mean of 45 marks and a standard deviation of 20 marks.

(a) Given that the pass mark is 41, estimate the number of candidates who passed the examination.

(b) If 5% of the candidates obtain a distinction by scoring x marks or more, estimate the value of x.

(c) Estimate the interquartile range of the distribution. (L. Additional)