Question #338419

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?

1
Expert's answer
2022-05-09T18:44:18-0400

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

i. A. P(X65)0.169P(X\geq65)\approx0.169

B. P(40X60)0.307P(40\leq X\leq60)\approx0.307

ii. A. P(X40)0.533P(X\geq40)\approx0.533. It means that approximately for 53.3%53.3\% of candidates the score exceeds 4040. Thus, 0.53310005330.533\cdot1000\approx533 candidates have the score that exceeds 4040.

B. P(40X65)0.364P(40\leq X\leq65)\approx0.364. Thus, 0.3641000=3640.364\cdot1000=364.

Answers: i. A. 0.1690.169, B. 0.3070.307; ii. A. 533533; B. 364364. (values in i. A and i. B are rounded to 33 decimal places).


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS