Answer to Question #338419 in Statistics and Probability for Sami

Question

An aptitude test for selecting officers in a bank was conducted on 1,000 candidates, the average score is 42 and the standard deviation of scores is 24. Assume that the scores are normally distributed, answer the following questions.

i. What is the probability that the candidates score,

A.Exceed 65?

B.Between 40 and 60?

ii. Find the number of candidates whose score,

A. Exceed 40?

B. Lie between 40 and 65?

Answer 1

Denote by $X$ a random variable that corresponds to a score of the selected person. It is normally distributed with parameters $\mu=42$ and $\sigma=24$. Find the probability:

i. A. $P(X\geq65)\approx0.169$

B. $P(40\leq X\leq60)\approx0.307$

ii. A. $P(X\geq40)\approx0.533$. It means that approximately for $53.3\%$ of candidates the score exceeds $40$. Thus, $0.533\cdot1000\approx533$ candidates have the score that exceeds $40$.

B. $P(40\leq X\leq65)\approx0.364$. Thus, $0.364\cdot1000=364$.

Answers: i. A. $0.169$, B. $0.307$; ii. A. $533$; B. $364$. (values in i. A and i. B are rounded to $3$ decimal places).