Answer to Question #272322 in Statistics and Probability for harshi

Question

An aptitude test for selecting officers in a bank was conducted on 1000 candidates. The average score is 42 and the standard deviation of scores is 24. Assuming normal distribution for the scores, find the number of candidates whose scores exceeds 58.

Answer 1

Let $X=$ the average score: $X\sim N(\mu, \sigma).$

Given $\mu=42, \sigma=24.$

$$P(X>58)=1-P(X\leq 58)$$

$$=1-P(X\leq \dfrac{58-42}{24})=1-P(X\leq\dfrac{2}{3})$$

$$\approx1-P(Z\leq0.6667)\approx0.25249$$

$$1000(0.25249)\approx252$$

The score of 252 candidates exceeds 58.